Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
241 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 70 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. C3×#4912 | C2 | semidirect |
| 2. C3×D3×D16 | C2 | semidirect |
| 3. C32×D32 | C2 | semidirect |
| 4. C3×#4520 | C2 | semidirect |
| 5. C3×#4519 | C2 | semidirect |
| 6. C3×#4449 | C2 | semidirect |
| 7. C3×#4447 | C2 | semidirect |
| 9. #69377 | C3 | direct (N × H) |
| 13. C32×D16 | C22 | semidirect |
| 16. C3×Dic24 | C22 | semidirect |
| 19. C32×C32 | C22 | semidirect |
| 20. C3×C3⋊C32 | C22 | semidirect |
| 23. #4912 | C2×C3 | semidirect |
| 24. D3×D16 | C2×C3 | semidirect |
| 29. C3×D32 | D3 | semidirect |
| 30. C3×D32 | C2×C3 | semidirect |
| 32. #4520 | C2×C3 | semidirect |
| 33. #4519 | C2×C3 | semidirect |
| 34. #4449 | C2×C3 | semidirect |
| 35. #4447 | C2×C3 | semidirect |
| 59. C3×D16 | C2×D3 | semidirect |
| 61. C3×D16 | C22×C3 | semidirect |
| 65. Dic24 | C22×C3 | semidirect |
| 70. C3×C32 | C2×D3 | semidirect |
| 71. C3×C32 | C22×C3 | semidirect |
| 72. C3⋊C32 | C22×C3 | semidirect |
| 89. D32 | C3×D3 | semidirect |
| 131. D16 | C2×C3×D3 | semidirect |
| 134. C32 | C2×C3×D3 | semidirect |
| 195. C32 | #2263 | semidirect |
| 229. C3 | #69377 | direct (N × H) |
| 230. C3 | C3×#2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4912 | 2 |
| C3×D3×D16 | 2 |
| C32×D32 | 2 |
| C3×#4520 | 2 |
| C3×#4519 | 2 |
| C3×#4449 | 2 |
| C3×#4447 | 2 |
| C3×#2263 | 3 |
| #69377 | 3 |