Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 129 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. #10592548 | C2 | semidirect |
| 4. C8×#634 | C2 | semidirect |
| 5. C32×#335 | C2 | semidirect |
| 7. #10589348 | C2 | semidirect |
| 28. C3×#335 | D3 | semidirect |
| 90. #335 | C3⋊D3 | semidirect |
| 193. C32 | #1682 | semidirect |
| 231. C3 | #68590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592548 | 2 |
| #10592547 | 2 |
| #10592393 | 2 |
| C8×#634 | 2 |
| C32×#335 | 2 |
| #10589351 | 2 |
| #10589348 | 2 |
| #68590 | 3 |