Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
462 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10588750 | C2 | semidirect |
| 3. #10588530 | C2 | semidirect |
| 4. #10588525 | C2 | semidirect |
| 5. C9×#331 | C2 | semidirect |
| 6. #10588162 | C2 | semidirect |
| 7. #10588162 | C2 | semidirect |
| 18. #63431 | C22 | semidirect |
| 19. C9×C4⋊C8 | C22 | semidirect |
| 20. C9×C4⋊C8 | C22 | semidirect |
| 25. C4×C9⋊C8 | C22 | semidirect |
| 100. D36 | SD16 | semidirect |
| 114. #331 | D9 | semidirect |
| 174. C4⋊C8 | C2×D9 | semidirect |
| 175. C4⋊C8 | C2×D9 | semidirect |
| 264. C9 | #1639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589819 | 2 |
| #10588750 | 2 |
| #10588530 | 2 |
| #10588525 | 2 |
| C9×#331 | 2 |
| #10588162 | 2 |
| #68392 | 3 |