Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
415 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 415 conjugacy classes of subgroups — too many to draw. Only its 94 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. #10592378 | C2 | semidirect |
| 3. #10590377 | C2 | semidirect |
| 4. C3×#4457 | C2 | semidirect |
| 5. #10589090 | C2 | semidirect |
| 29. #4457 | D3 | semidirect |
| 86. C32×C8 | SD16 | semidirect |
| 188. C3×C8 | #204 | semidirect |
| 189. C3×C8 | #214 | semidirect |
| 240. C32 | #1688 | semidirect |
| 256. C8 | #3716 | semidirect |
| 279. C3 | #68550 | semidirect |
| 280. C3 | #71287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592378 | 2 |
| C3×#4695 | 2 |
| #10590377 | 2 |
| C3×#4457 | 2 |
| #10589090 | 2 |
| #71287 | 3 |
| #68550 | 3 |