Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
266 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 82 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. C32×#508 | C2 | semidirect |
| 2. C2×C3×D48 | C2 | semidirect |
| 3. C3×#4521 | C2 | semidirect |
| 4. C3×#4519 | C2 | semidirect |
| 5. C3×#4499 | C2 | semidirect |
| 7. #71509 | C3 | direct (N × H) |
| 10. C32×Q32 | C22 | semidirect |
| 12. C32×D16 | C22 | semidirect |
| 16. C3×C3⋊C32 | C22 | semidirect |
| 18. C3×#508 | D3 | semidirect |
| 19. C3×#508 | C2×C3 | semidirect |
| 21. C2×D48 | C2×C3 | semidirect |
| 25. #4521 | C2×C3 | semidirect |
| 26. #4519 | C2×C3 | semidirect |
| 27. #4499 | C2×C3 | semidirect |
| 45. C3×Q32 | C2×D3 | semidirect |
| 46. C3×Q32 | C22×C3 | semidirect |
| 53. C3×D16 | C2×D3 | semidirect |
| 54. C3×D16 | C22×C3 | semidirect |
| 61. C3⋊C32 | C22×C3 | semidirect |
| 72. #508 | C3×D3 | semidirect |
| 113. Q32 | C2×C3×D3 | semidirect |
| 117. D16 | C2×C3×D3 | semidirect |
| 180. C32 | #2263 | semidirect |
| 210. C3 | #71509 | direct (N × H) |
| 211. C3 | C3×#2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#508 | 2 |
| C2×C3×D48 | 2 |
| C3×#4521 | 2 |
| C3×#4519 | 2 |
| C3×#4499 | 2 |
| C3×#2263 | 3 |
| #71509 | 3 |