Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
223 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 74 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×#909 | C2 | semidirect |
| 3. C2×C3×#204 | C2 | semidirect |
| 4. C3×#901 | C2 | semidirect |
| 5. C32×#108 | C2 | semidirect |
| 6. C3×#824 | C2 | semidirect |
| 7. C3×#823 | C2 | semidirect |
| 9. #4898 | C3 | direct (N × H) |
| 29. #909 | C2×C3 | semidirect |
| 31. C2×#204 | C2×C3 | semidirect |
| 32. #901 | C2×C3 | semidirect |
| 34. C3×#108 | D3 | semidirect |
| 35. C3×#108 | C2×C3 | semidirect |
| 38. #824 | C2×C3 | semidirect |
| 39. #823 | C2×C3 | semidirect |
| 102. #108 | C3×D3 | semidirect |
| 180. C32 | #471 | semidirect |
| 216. C3 | #4898 | direct (N × H) |
| 217. C3 | C3×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#909 | 2 |
| C3×#908 | 2 |
| C2×C3×#204 | 2 |
| C3×#901 | 2 |
| C32×#108 | 2 |
| C3×#824 | 2 |
| C3×#823 | 2 |
| C3×#471 | 3 |
| #4898 | 3 |