Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
285 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 82 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. C9×#487 | C2 | semidirect |
| 4. #10588766 | C2 | semidirect |
| 5. #10588760 | C2 | semidirect |
| 7. C8×C9⋊C8 | C2 | semidirect |
| 79. #487 | D9 | semidirect |
| 170. C9 | #1708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#487 | 2 |
| #10588773 | 2 |
| #10588770 | 2 |
| #10588766 | 2 |
| #10588760 | 2 |
| #10588376 | 2 |
| C8×C9⋊C8 | 2 |
| #71213 | 3 |