Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
322 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10590173 | C2 | semidirect |
| 5. #10590172 | C2 | semidirect |
| 6. #10590171 | C2 | semidirect |
| 7. #10590170 | C2 | semidirect |
| 41. #3743 | C8 | semidirect |
| 67. C32×C8 | C2×C8 | semidirect |
| 69. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 167. C32 | #1565 | semidirect |
| 187. C8 | #3787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593727 | 2 |
| #10593726 | 2 |
| #10592406 | 2 |
| #10590173 | 2 |
| #10590172 | 2 |
| #10590171 | 2 |
| #10590170 | 2 |
| #1565 | 9 |