Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
690 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 183 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. C32×#424 | C2 | semidirect |
| 4. C2×C8×C3⋊Dic3 | C2 | semidirect |
| 6. #10589424 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 20. #63637 | C4 | semidirect |
| 21. #63636 | C4 | semidirect |
| 22. C3×#424 | D3 | semidirect |
| 94. #424 | C3⋊D3 | semidirect |
| 223. C32 | #1937 | semidirect |
| 266. C3 | #70535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#424 | 2 |
| C2×#63652 | 2 |
| #10592809 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| #10592701 | 2 |
| #10589424 | 2 |
| #10589398 | 2 |
| #70535 | 3 |