Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
462 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 72 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. C9×#393 | C2 | semidirect |
| 3. #10588908 | C2 | semidirect |
| 4. #10588202 | C2 | semidirect |
| 5. #10588129 | C2 | semidirect |
| 7. C22×Q8×C9 | C22 | semidirect |
| 17. C9×#95 | C22 | semidirect |
| 19. #63389 | C22 | semidirect |
| 66. C23×C9 | SD16 | semidirect |
| 94. #393 | D9 | semidirect |
| 139. C22×Q8 | C2×D9 | semidirect |
| 151. #95 | C2×D9 | semidirect |
| 231. C9 | #1601 | semidirect |
| 240. C23 | #3675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589595 | 2 |
| C9×#393 | 2 |
| #10588908 | 2 |
| #10588202 | 2 |
| #10588129 | 2 |
| #69699 | 3 |