Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
156 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 56 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. C2×Dic72 | C2 | semidirect |
| 3. C9×M64 | C2 | semidirect |
| 4. Dic144 | C2 | semidirect |
| 5. #10588126 | C2 | semidirect |
| 55. M64 | D9 | semidirect |
| 110. C9 | #2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic72 | 2 |
| #10588584 | 2 |
| C9×M64 | 2 |
| Dic144 | 2 |
| #10588126 | 2 |
| #69374 | 3 |