Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1074 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 253 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. #10592548 | C2 | semidirect |
| 5. #10592528 | C2 | semidirect |
| 8. #10592415 | C2 | semidirect |
| 9. C4×#3746 | C2 | semidirect |
| 250. C32 | #3127 | semidirect |
| 283. C3 | #79396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595989 | 2 |
| #10595987 | 2 |
| C32×#433 | 2 |
| #10592548 | 2 |
| #10592528 | 2 |
| #10592438 | 2 |
| #10592422 | 2 |
| #10592415 | 2 |
| C4×#3746 | 2 |
| #79396 | 3 |