6. Among the 8 vertices, 6 centers of the faces (bottom faces), and the center of the body, a total of 15 points, if a plane formed by any 3 different and non-collinear points is perpendicular to a line formed by another 2 different points, then these 5 points are called an "orthogonal 5-point group". Therefore, the total number of orthogonal 5-point groups formed by these 15 points is ( ).
(A)366
(B) 516
(C) 1428
(D) 1824
6.D.

As shown in Figure 6, let $O$ be the center of the body, and $O_{i} (i = 1,2, \cdots, 6)$ be the centers of the respective faces.

Classify and discuss according to the plane formed by the 3 points (referred to as the "3-point plane").

Observation shows that there are only 4 possible 3-point planes: side faces (such as $A_{1} B_{1} C_{1} D_{1}$), diagonal faces (such as $A_{1} C_{1} C A$), equilateral triangles formed by three vertices (such as $\triangle A B_{1} C$), and central faces (such as $O_{3} O_{5} O_{4} O_{6}$).
(1) When the side face is $A_{1} B_{1} C_{1} D_{1}$, the points $A_{1}, B_{1}, C_{1}, D_{1}$ can form 4 non-collinear 3-point groups (3-point planes, hereinafter the same), and the points $O_{2}, O, O_{1}$ can form 3 2-point groups. Thus, the 3-point groups and 2-point groups can combine to form $4 \times 3 = 12$ orthogonal 5-point groups. Additionally, by taking point $O_{1}$ and any two points from $\{A_{1}, B_{1}, C_{1}, D_{1}\}$, 4 non-collinear 3-point groups can be formed. For example, $\{O_{1}, A_{1}, B_{1}\}$, and the 2-point groups perpendicular to this 3-point group are $\{O_{2}, O\}$, $\{D, D_{1}\}$, $\{C, C_{1}\}$. Therefore, $4 \times 3 = 12$ orthogonal 5-point groups can be formed.

Noting that there are 6 side faces, the total number of orthogonal 5-point groups formed by 3-point groups from side faces is $6 \times (12 + 12) = 144$.
(2) When the diagonal face is $A_{1} C_{1} C A$, the 3-point groups formed by $\{A, A_{1}, C_{1}, C, O_{1}, O, O_{2}\}$ can form $\left(C_{7}^{3} - 5\right) \times 4 + \left(C_{6}^{3} - 3\right) \times 4 = 188$ orthogonal 5-point groups.

Since there are 6 diagonal faces, a total of $6 \times 188 = 1128$ orthogonal 5-point groups of this type are formed.
(3) When the equilateral triangle is $\triangle A B_{1} C$, the 3-point groups are formed by $\{A, B_{1}, C, O_{2}, O_{3}, O_{5}\}$, and the 2-point groups are formed by $\{D_{1}, O, B\}$. Therefore, there are $\left(C_{6}^{3} - 3\right) \times C_{3}^{2} = 51$ orthogonal 5-point groups.

Since there are 8 equilateral triangles, a total of $8 \times 51 = 408$ orthogonal 5-point groups of this type are formed.
(4) When the central face is $O_{3} O_{5} O_{4} O_{6}$, the 3-point groups are formed by $\{O, O_{3}, O_{5}, O_{4}, O_{6}\}$, and there are $\left(C_{5}^{3} - 2\right) \times 5 + C_{4}^{3} \times 2 = 48$ orthogonal 5-point groups.

Since there are 3 central faces, a total of $48 \times 3 = 144$ orthogonal 5-point groups of this type are formed.
In summary, there are a total of $144 + 1128 + 408 + 144 = 1824$ orthogonal 5-point groups.