Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
417 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10589585 | C2 | semidirect |
| 5. C9×#342 | C2 | semidirect |
| 6. #10588204 | C2 | semidirect |
| 7. #10588203 | C2 | semidirect |
| 30. C23×D9 | Q8 | semidirect |
| 43. C22×Dic9 | Q8 | semidirect |
| 111. #342 | D9 | semidirect |
| 276. C9 | #2032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589585 | 2 |
| C2×#63365 | 2 |
| C9×#342 | 2 |
| #10588204 | 2 |
| #10588203 | 2 |
| #68967 | 3 |