Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
543 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 100 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×#63506 | C2 | semidirect |
| 4. C9×#419 | C2 | semidirect |
| 6. C2×#63382 | C2 | semidirect |
| 7. #10588208 | C2 | semidirect |
| 139. #419 | D9 | semidirect |
| 314. C9 | #2005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63506 | 2 |
| C2×#63505 | 2 |
| #10589628 | 2 |
| C9×#419 | 2 |
| C2×#63384 | 2 |
| C2×#63382 | 2 |
| #10588208 | 2 |
| #70346 | 3 |