Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10588522 | C2 | semidirect |
| 3. C9×#334 | C2 | semidirect |
| 4. #10588162 | C2 | semidirect |
| 5. #10588132 | C2 | semidirect |
| 56. C8×C9 | M16 | semidirect |
| 61. #334 | D9 | semidirect |
| 134. C9 | #1594 | semidirect |
| 148. C8 | #3663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588522 | 2 |
| C4×D72 | 2 |
| C9×#334 | 2 |
| #10588162 | 2 |
| #10588132 | 2 |
| #68525 | 3 |