Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
963 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 963 conjugacy classes of subgroups — too many to draw. Only its 180 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. #10593907 | C2 | semidirect |
| 2. C4×#3743 | C2 | semidirect |
| 3. C3×#4695 | C2 | semidirect |
| 4. C3×#4680 | C2 | semidirect |
| 5. #10590846 | C2 | semidirect |
| 6. #10590781 | C2 | semidirect |
| 7. #10590277 | C2 | semidirect |
| 36. #4695 | D3 | semidirect |
| 40. #4680 | D3 | semidirect |
| 114. C32×C8 | #41 | semidirect |
| 236. C3×C8 | #237 | semidirect |
| 237. C3×C8 | #239 | semidirect |
| 294. C32 | #3184 | semidirect |
| 311. C8 | #3796 | semidirect |
| 335. C3 | #81777 | semidirect |
| 336. C3 | #81888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593907 | 2 |
| C4×#3743 | 2 |
| C3×#4695 | 2 |
| C3×#4680 | 2 |
| #10590846 | 2 |
| #10590781 | 2 |
| #10590277 | 2 |
| #81888 | 3 |
| #81777 | 3 |