Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
297 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 297 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×#500 | C2 | semidirect |
| 4. #10588765 | C2 | semidirect |
| 5. #10588758 | C2 | semidirect |
| 7. #10588131 | C2 | semidirect |
| 78. #500 | D9 | semidirect |
| 173. C9 | #1722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#500 | 2 |
| #10588773 | 2 |
| #10588770 | 2 |
| #10588765 | 2 |
| #10588758 | 2 |
| #10588376 | 2 |
| #10588131 | 2 |
| #71366 | 3 |