Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
273 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 273 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. C3×#936 | C2 | semidirect |
| 3. C2×C3×#204 | C2 | semidirect |
| 4. C3×#893 | C2 | semidirect |
| 5. C32×#102 | C2 | semidirect |
| 6. C3×Dic3⋊C8 | C2 | semidirect |
| 7. C3×#810 | C2 | semidirect |
| 9. #4787 | C3 | direct (N × H) |
| 27. #936 | C2×C3 | semidirect |
| 29. C2×#204 | C2×C3 | semidirect |
| 30. #893 | C2×C3 | semidirect |
| 34. C3×#102 | D3 | semidirect |
| 35. C3×#102 | C2×C3 | semidirect |
| 36. Dic3⋊C8 | C2×C3 | semidirect |
| 37. #810 | C2×C3 | semidirect |
| 103. #102 | C3×D3 | semidirect |
| 193. C32 | #463 | semidirect |
| 238. C3 | #4787 | direct (N × H) |
| 239. C3 | C3×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#936 | 2 |
| C2×C3×#213 | 2 |
| C2×C3×#204 | 2 |
| C3×#893 | 2 |
| C32×#102 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#810 | 2 |
| C3×#463 | 3 |
| #4787 | 3 |