Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
381 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 381 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×C3×#827 | C2 | semidirect |
| 3. C2×C3×#800 | C2 | semidirect |
| 4. C3×#4873 | C2 | semidirect |
| 5. C32×#357 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. C3×#4491 | C2 | semidirect |
| 9. #69204 | C3 | direct (N × H) |
| 28. C2×#827 | C2×C3 | semidirect |
| 29. C2×#800 | C2×C3 | semidirect |
| 30. #4873 | C2×C3 | semidirect |
| 34. C3×#357 | D3 | semidirect |
| 35. C3×#357 | C2×C3 | semidirect |
| 36. Dic3⋊C16 | C2×C3 | semidirect |
| 37. #4491 | C2×C3 | semidirect |
| 53. C3×Dic12 | D4 | semidirect |
| 112. #357 | C3×D3 | semidirect |
| 151. Dic12 | C3×D4 | semidirect |
| 171. C3×Dic3 | SD32 | semidirect |
| 285. Dic3 | C3×SD32 | semidirect |
| 286. C32 | #2207 | semidirect |
| 333. C3 | #69204 | direct (N × H) |
| 334. C3 | C3×#2207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5151 | 2 |
| C2×C3×#827 | 2 |
| C2×C3×#800 | 2 |
| C3×#4873 | 2 |
| C32×#357 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4491 | 2 |
| C3×#2207 | 3 |
| #69204 | 3 |