Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
402 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 61 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. #10593554 | C2 | semidirect |
| 5. C2×#63746 | C2 | semidirect |
| 6. C2×#63744 | C2 | semidirect |
| 7. #10590093 | C2 | semidirect |
| 233. C32 | #2067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593827 | 2 |
| C2×#63782 | 2 |
| #10593554 | 2 |
| C2×#63746 | 2 |
| C2×#63744 | 2 |
| #10590093 | 2 |
| #2067 | 9 |