Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
867 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 867 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 2. #10589588 | C2 | semidirect |
| 3. #10588635 | C2 | semidirect |
| 4. #10588635 | C2 | semidirect |
| 5. C2×#63365 | C2 | semidirect |
| 6. C9×#342 | C2 | semidirect |
| 7. #10588204 | C2 | semidirect |
| 22. #63444 | C4 | semidirect |
| 42. C23×D9 | C2×C4 | semidirect |
| 46. C22×C4×C9 | D4 | semidirect |
| 55. C22×Dic9 | D4 | semidirect |
| 64. C9×C22⋊C4 | C2×C4 | semidirect |
| 122. C22×D9 | C22⋊C4 | semidirect |
| 139. C2×Dic9 | C22⋊C4 | semidirect |
| 148. #342 | D9 | semidirect |
| 325. C22×C4 | D36 | semidirect |
| 340. C22⋊C4 | C4×D9 | semidirect |
| 377. C9 | #1889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63444 | 2 |
| #10589588 | 2 |
| #10588635 | 2 |
| C2×#63365 | 2 |
| C9×#342 | 2 |
| #10588204 | 2 |
| #68962 | 3 |