title: Rod group
text: # Rod group
  
  In mathematics, a rod group is a three-dimensional line group whose point group is one of the axial crystallographic point groups. This constraint means that the point group must be the symmetry of some three-dimensional lattice.
  
  Table of the 75 rod groups, organized by crystal system or lattice type, and by their point groups:
  
  Triclinic :
  
  | 1 | p1 | 2 | p1 |
  | - | - | - | - |
  | Monoclinic/inclined ||||||||||
  | 3 | p211 | 4 | pm11 | 5 | pc11 | 6 | p2/m11 | 7 | p2/c11 |
  | Monoclinic/orthogonal ||||||||||
  | 8 | p112 | 9 | $p112_1$ | 10 | p11m | 11 | p112/m | 12 | $p112_1/m$ |
  | Orthorhombic ||||||||||
  | 13 | p222 | 14 | $p222_1$ | 15 | pmm2 | 16 | pcc2 | 17 | $pmc2_1$ |
  | 18 | p2mm | 19 | p2cm | 20 | pmmm | 21 | pccm | 22 | pmcm |
  | Tetragonal ||||||||||
  | 23 | p4 | 24 | $p4_1$ | 25 | $p4_2$ | 26 | $p4_3$ | 27 | p4 |
  | 28 | p4/m | 29 | $p4_2/m$ | 30 | p422 | 31 | $p4_122$ | 32 | $p4_222$ |
  | 33 | $p4_322$ | 34 | p4mm | 35 | $p4_2cm,$ $p4_2mc$ | 36 | p4cc | 37 | p42m, p4m2 |
  | 38 | p42c, p4c2 | 39 | p4/mmm | 40 | p4/mcc | 41 | $p4_2/mmc,$ $p4_2/mcm$ |
  | Trigonal ||||||||||
  | 42 | p3 | 43 | $p3_1$ | 44 | $p3_2$ | 45 | p3 | 46 | p312, p321 |
  | 47 | $p3_112,$ $p3_121$ | 48 | $p3_212,$ $p3_221$ | 49 | p3m1, p31m | 50 | p3c1, p31c | 51 | p3m1, p31m |
  | 52 | p3c1, p31c |
  | Hexagonal ||||||||||
  | 53 | p6 | 54 | $p6_1$ | 55 | $p6_2$ | 56 | $p6_3$ | 57 | $p6_4$ |
  | 58 | $p6_5$ | 59 | p6 | 60 | p6/m | 61 | $p6_3/m$ | 62 | p622 |
  | 63 | $p6_122$ | 64 | $p6_222$ | 65 | $p6_322$ | 66 | $p6_422$ | 67 | $p6_522$ |
  | 68 | p6mm | 69 | p6cc | 70 | $p6_3mc,$ $p6_3cm$ | 71 | p6m2, p62m | 72 | p6c2, p62c |
  | 73 | p6/mmm | 74 | p6/mcc | 75 | $p6_3/mmc,$ $p6_3/mcm$ |
  
  The double entries are for orientation variants of a group relative to the perpendicular-directions lattice.
  
  Among these groups, there are 8 enantiomorphic pairs.
  
  