Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 12. #64078 | C4 | semidirect |
| 13. #64078 | C4 | semidirect |
| 15. C4×#634 | C4 | semidirect |
| 186. C32 | #1506 | semidirect |
| 222. C3 | #70836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595941 | 2 |
| C32×#432 | 2 |
| #10592631 | 2 |
| #10589333 | 2 |
| #70836 | 3 |