Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10592381 | C2 | semidirect |
| 4. C3×#4458 | C2 | semidirect |
| 5. #10589096 | C2 | semidirect |
| 29. #4458 | D3 | semidirect |
| 227. C32 | #1675 | semidirect |
| 266. C3 | #68579 | semidirect |
| 267. C3 | #70853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592381 | 2 |
| C3×C8×D12 | 2 |
| #10590268 | 2 |
| C3×#4458 | 2 |
| #10589096 | 2 |
| #70853 | 3 |
| #68579 | 3 |