Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1236 conjugacy classes of subgroups; only the 385 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 385 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 |
|---|---|---|
| 2. C2×C32×#97 | C2 | semidirect |
| 4. C2×#63641 | C2 | semidirect |
| 5. C2×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 6. #10592408 | C2 | direct (N × H) |
| 17. C32×#97 | C22 | semidirect |
| 19. #63641 | C22 | semidirect |
| 20. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 22. C2×C3×#97 | D3 | semidirect |
| 55. C3×#97 | C2×D3 | semidirect |
| 80. C2×#97 | C3⋊D3 | semidirect |
| 122. #97 | C2×C3⋊D3 | semidirect |
| 141. C2×C32 | #433 | semidirect |
| 174. C32 | C2×#433 | semidirect |
| 192. C2×C3 | #4709 | semidirect |
| 207. C3 | C2×#4709 | semidirect |
| 209. C2 | #10592408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64081 | 2 |
| C2×C32×#97 | 2 |
| C2×#63647 | 2 |
| C2×#63641 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #10592408 | 2 |
| C2×#4709 | 3 |