Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
672 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#500 | C2 | semidirect |
| 2. #10592787 | C2 | semidirect |
| 3. #10592784 | C2 | semidirect |
| 5. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 16. C3×#500 | D3 | semidirect |
| 52. C32×C8 | SD16 | semidirect |
| 54. C3⋊(C3⋊C8) | D8 | semidirect |
| 55. #500 | C3⋊D3 | semidirect |
| 98. C3×C8 | #215 | semidirect |
| 125. C32 | #1706 | semidirect |
| 137. C8 | #3755 | semidirect |
| 150. C3 | #71359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| #10592787 | 2 |
| #10592784 | 2 |
| #10592394 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71359 | 3 |