Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
239 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 78 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×#131 | C2 | semidirect |
| 2. C3×#951 | C2 | semidirect |
| 4. C2×C3×#204 | C2 | semidirect |
| 5. C3×#824 | C2 | semidirect |
| 6. C3×#823 | C2 | semidirect |
| 7. C3×#819 | C2 | semidirect |
| 9. #5141 | C3 | direct (N × H) |
| 29. C3×#131 | D3 | semidirect |
| 30. C3×#131 | C2×C3 | semidirect |
| 31. #951 | C2×C3 | semidirect |
| 33. C2×#204 | C2×C3 | semidirect |
| 37. #824 | C2×C3 | semidirect |
| 38. #823 | C2×C3 | semidirect |
| 39. #819 | C2×C3 | semidirect |
| 103. #131 | C3×D3 | semidirect |
| 187. C32 | #471 | semidirect |
| 224. C3 | #5141 | direct (N × H) |
| 225. C3 | C3×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#131 | 2 |
| C3×#951 | 2 |
| C3×#949 | 2 |
| C2×C3×#204 | 2 |
| C3×#824 | 2 |
| C3×#823 | 2 |
| C3×#819 | 2 |
| C3×#471 | 3 |
| #5141 | 3 |