Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
371 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 86 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×#5151 | C2 | semidirect |
| 2. C3×#5147 | C2 | semidirect |
| 3. C3×#4908 | C2 | semidirect |
| 4. C3×#4895 | C2 | semidirect |
| 5. C32×#361 | C2 | semidirect |
| 6. C3×#4511 | C2 | semidirect |
| 7. C3×#4495 | C2 | semidirect |
| 9. #69263 | C3 | direct (N × H) |
| 29. #5151 | C2×C3 | semidirect |
| 30. #5147 | C2×C3 | semidirect |
| 31. #4908 | C2×C3 | semidirect |
| 32. #4895 | C2×C3 | semidirect |
| 36. C3×#361 | D3 | semidirect |
| 37. C3×#361 | C2×C3 | semidirect |
| 38. #4511 | C2×C3 | semidirect |
| 39. #4495 | C2×C3 | semidirect |
| 52. C3×Dic12 | D4 | semidirect |
| 55. C3×D24 | D4 | semidirect |
| 119. #361 | C3×D3 | semidirect |
| 156. Dic12 | C3×D4 | semidirect |
| 159. D24 | C3×D4 | semidirect |
| 287. C32 | #2213 | semidirect |
| 330. C3 | #69263 | direct (N × H) |
| 331. C3 | C3×#2213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5151 | 2 |
| C3×#5147 | 2 |
| C3×#4908 | 2 |
| C3×#4895 | 2 |
| C32×#361 | 2 |
| C3×#4511 | 2 |
| C3×#4495 | 2 |
| C3×#2213 | 3 |
| #69263 | 3 |