Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
435 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 435 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10592775 | C2 | semidirect |
| 3. #10590339 | C2 | semidirect |
| 4. #10590272 | C2 | semidirect |
| 5. C3×#4544 | C2 | semidirect |
| 6. #10589100 | C2 | semidirect |
| 7. #10589094 | C2 | semidirect |
| 35. #4544 | D3 | semidirect |
| 115. C3⋊(C3⋊C8) | D8 | semidirect |
| 329. C32 | #1685 | semidirect |
| 382. C3 | #68398 | semidirect |
| 383. C3 | #71008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592775 | 2 |
| C3×#5072 | 2 |
| #10590339 | 2 |
| #10590272 | 2 |
| C3×#4544 | 2 |
| #10589100 | 2 |
| #10589094 | 2 |
| #71008 | 3 |
| #68398 | 3 |