Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
867 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 867 conjugacy classes of subgroups — too many to draw. Only its 130 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×#518 | C2 | semidirect |
| 3. C2×#63393 | C2 | semidirect |
| 4. #10588635 | C2 | semidirect |
| 5. #10588203 | C2 | semidirect |
| 17. #63499 | C4 | semidirect |
| 33. C23×D9 | C2×C4 | semidirect |
| 40. C22×C4×C9 | D4 | semidirect |
| 53. #3676 | C2×C4 | semidirect |
| 75. C23×C9 | C22⋊C4 | semidirect |
| 100. C2×C4×C9 | C22⋊C4 | semidirect |
| 107. #518 | D9 | semidirect |
| 242. C22×C4 | #611 | semidirect |
| 280. C9 | #1889 | semidirect |
| 297. C23 | (C2×D9)⋊C4 | semidirect |
| 315. C2×C4 | (C2×D9)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#518 | 2 |
| C2×#63499 | 2 |
| C2×#63393 | 2 |
| #10588635 | 2 |
| #10588203 | 2 |
| #71654 | 3 |