Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
696 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 696 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 |
|---|---|---|
| 4. #10592696 | C2 | semidirect |
| 5. #10592694 | C2 | semidirect |
| 6. #10589424 | C2 | semidirect |
| 7. #10589420 | C2 | semidirect |
| 18. #63660 | C4 | semidirect |
| 246. C32 | #1931 | semidirect |
| 295. C3 | #70318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#418 | 2 |
| C2×#63660 | 2 |
| C2×#63659 | 2 |
| #10592696 | 2 |
| #10592694 | 2 |
| #10589424 | 2 |
| #10589420 | 2 |
| #70318 | 3 |