Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
963 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 963 conjugacy classes of subgroups — too many to draw. Only its 162 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. #10593972 | C2 | semidirect |
| 2. #10592406 | C2 | semidirect |
| 3. C3×#4711 | C2 | semidirect |
| 4. #10590900 | C2 | semidirect |
| 5. #10590886 | C2 | semidirect |
| 6. #10590885 | C2 | semidirect |
| 7. #10590846 | C2 | semidirect |
| 8. #10590840 | C2 | semidirect |
| 9. #10590344 | C2 | semidirect |
| 41. #4711 | D3 | semidirect |
| 121. C32×C8 | #41 | semidirect |
| 123. C3⋊(C3⋊C8) | #41 | semidirect |
| 242. C3×C8 | #235 | semidirect |
| 299. C32 | #3184 | semidirect |
| 320. C8 | #3798 | semidirect |
| 342. C3 | #79877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593972 | 2 |
| #10592406 | 2 |
| C3×#4711 | 2 |
| #10590900 | 2 |
| #10590886 | 2 |
| #10590885 | 2 |
| #10590846 | 2 |
| #10590840 | 2 |
| #10590344 | 2 |
| #79877 | 3 |