Mg14LaGa crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Ga cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Ga cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Ga cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)LaMg10Ga cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)LaMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 11-coordinate geometry to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent La(1), and one Ga(1) atom. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)LaMg10Ga cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with eight equivalent Mg(5)LaMg10Ga cuboctahedra. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one La(1), and one Ga(1) atom to form distorted MgLaMg10Ga cuboctahedra that share corners with four equivalent Mg(6)LaMg11 cuboctahedra, corners with ten equivalent Mg(5)LaMg10Ga cuboctahedra, edges with two equivalent Mg(5)LaMg10Ga cuboctahedra, edges with two equivalent Mg(6)LaMg11 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Ga2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with four equivalent Mg(5)LaMg10Ga cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one La(1) atom to form distorted MgLaMg11 cuboctahedra that share corners with six equivalent Mg(6)LaMg11 cuboctahedra, corners with eight equivalent Mg(5)LaMg10Ga cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)LaMg10Ga cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Ga cuboctahedra. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Ga(1) atom. La(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Ga(1) atoms to form LaMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent La(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Ga cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Ga cuboctahedra. Ga(1) is bonded in a 10-coordinate geometry to two equivalent Mg(3), two equivalent Mg(7), four equivalent Mg(5), and two equivalent La(1) atoms.
Mg14LaGa crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Ga cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent La(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(5)LaMg10Ga cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.18 Å. Both Mg(1)-Mg(6) bond lengths are 3.13 Å. There are two shorter (3.28 Å) and two longer (3.31 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5) bond lengths are 3.14 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Ga cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(5)LaMg10Ga cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(6)LaMg11 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.31 Å. There are two shorter (3.24 Å) and two longer (3.35 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5) bond lengths are 3.13 Å. In the third Mg site, Mg(3) is bonded in a 11-coordinate geometry to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent La(1), and one Ga(1) atom. There is one shorter (3.09 Å) and one longer (3.28 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.18 Å. Both Mg(3)-Mg(6) bond lengths are 3.31 Å. Both Mg(3)-Mg(7) bond lengths are 3.14 Å. There is one shorter (3.29 Å) and one longer (3.30 Å) Mg(3)-La(1) bond length. The Mg(3)-Ga(1) bond length is 2.95 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent La(1)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(5)LaMg10Ga cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with eight equivalent Mg(5)LaMg10Ga cuboctahedra. There is one shorter (3.11 Å) and one longer (3.26 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.14 Å. Both Mg(4)-Mg(6) bond lengths are 3.09 Å. Both Mg(4)-Mg(7) bond lengths are 3.36 Å. In the fifth Mg site, Mg(5) is bonded to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), one La(1), and one Ga(1) atom to form distorted MgLaMg10Ga cuboctahedra that share corners with four equivalent Mg(6)LaMg11 cuboctahedra, corners with ten equivalent Mg(5)LaMg10Ga cuboctahedra, edges with two equivalent Mg(5)LaMg10Ga cuboctahedra, edges with two equivalent Mg(6)LaMg11 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Ga2 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with four equivalent Mg(5)LaMg10Ga cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (3.14 Å) and one longer (3.23 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.22 Å) and one longer (3.36 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.24 Å) and one longer (3.36 Å) Mg(5)-Mg(7) bond length. The Mg(5)-La(1) bond length is 3.32 Å. The Mg(5)-Ga(1) bond length is 3.19 Å. In the sixth Mg site, Mg(6) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one La(1) atom to form distorted MgLaMg11 cuboctahedra that share corners with six equivalent Mg(6)LaMg11 cuboctahedra, corners with eight equivalent Mg(5)LaMg10Ga cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent La(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(5)LaMg10Ga cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(1)Mg12 cuboctahedra,  a faceface with one La(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Ga cuboctahedra. Both Mg(6)-Mg(7) bond lengths are 3.20 Å. The Mg(6)-La(1) bond length is 3.28 Å. In the seventh Mg site, Mg(7) is bonded in a distorted single-bond geometry to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Ga(1) atom. The Mg(7)-Ga(1) bond length is 3.15 Å. La(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Ga(1) atoms to form LaMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent La(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(6)LaMg11 cuboctahedra, edges with eight equivalent Mg(5)LaMg10Ga cuboctahedra, faces with two equivalent Mg(6)LaMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(5)LaMg10Ga cuboctahedra. Both La(1)-Ga(1) bond lengths are 3.20 Å. Ga(1) is bonded in a 10-coordinate geometry to two equivalent Mg(3), two equivalent Mg(7), four equivalent Mg(5), and two equivalent La(1) atoms.