Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
243 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 16. #63375 | C4 | semidirect |
| 17. C8×Dic9 | C4 | semidirect |
| 180. C9 | #1841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×Dic9 | 2 |
| C9×#344 | 2 |
| #10588236 | 2 |
| #10588235 | 2 |
| C9⋊#338 | 2 |
| #10588210 | 2 |
| #10588208 | 2 |
| #69017 | 3 |