Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
362 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 362 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. C2×C3×#237 | C2 | semidirect |
| 2. C2×C32×D8 | C2 | semidirect |
| 3. C3×#938 | C2 | semidirect |
| 4. C2×C3×#214 | C2 | semidirect |
| 5. C3×#832 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C3×#816 | C2 | semidirect |
| 9. #5158 | C3 | direct (N × H) |
| 26. C2×#237 | C2×C3 | semidirect |
| 29. C2×C3×D8 | D3 | semidirect |
| 30. C2×C3×D8 | C2×C3 | semidirect |
| 32. #938 | C2×C3 | semidirect |
| 33. C2×#214 | C2×C3 | semidirect |
| 37. #832 | C2×C3 | semidirect |
| 38. (C2×D3)⋊C8 | C2×C3 | semidirect |
| 39. #816 | C2×C3 | semidirect |
| 46. C32×D4 | D4 | semidirect |
| 57. C3×Dic6 | D4 | semidirect |
| 112. C2×D8 | C3×D3 | semidirect |
| 139. C3×D4 | #67 | semidirect |
| 140. C3×D4 | C3×D4 | semidirect |
| 159. Dic6 | C3×D4 | semidirect |
| 225. C32 | #449 | semidirect |
| 236. D4 | C3×#67 | semidirect |
| 279. C3 | #5158 | direct (N × H) |
| 280. C3 | C3×#449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#237 | 2 |
| C2×C32×D8 | 2 |
| C3×#938 | 2 |
| C2×C3×#214 | 2 |
| C3×#832 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#816 | 2 |
| C3×#449 | 3 |
| #5158 | 3 |