Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 149 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×C8×Q8 | C2 | semidirect |
| 2. #10592730 | C2 | semidirect |
| 5. #10589352 | C2 | semidirect |
| 7. #10589324 | C2 | semidirect |
| 24. C3×C8×Q8 | D3 | semidirect |
| 89. C8×Q8 | C3⋊D3 | semidirect |
| 193. C32 | #1682 | semidirect |
| 231. C3 | #70941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| #10592730 | 2 |
| #10592726 | 2 |
| #10592393 | 2 |
| #10589352 | 2 |
| #10589351 | 2 |
| #10589324 | 2 |
| #70941 | 3 |