Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
269 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 269 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×#947 | C2 | semidirect |
| 2. C2×C3×#215 | C2 | semidirect |
| 4. C3×#893 | C2 | semidirect |
| 5. C32×#103 | C2 | semidirect |
| 6. C3×Dic3⋊C8 | C2 | semidirect |
| 7. C3×#809 | C2 | semidirect |
| 9. #4819 | C3 | direct (N × H) |
| 27. #947 | C2×C3 | semidirect |
| 28. C2×#215 | C2×C3 | semidirect |
| 30. #893 | C2×C3 | semidirect |
| 33. C3×#103 | D3 | semidirect |
| 34. C3×#103 | C2×C3 | semidirect |
| 36. Dic3⋊C8 | C2×C3 | semidirect |
| 37. #809 | C2×C3 | semidirect |
| 102. #103 | C3×D3 | semidirect |
| 191. C32 | #463 | semidirect |
| 235. C3 | #4819 | direct (N × H) |
| 236. C3 | C3×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#947 | 2 |
| C2×C3×#215 | 2 |
| C2×C3×D24 | 2 |
| C3×#893 | 2 |
| C32×#103 | 2 |
| C3×Dic3⋊C8 | 2 |
| C3×#809 | 2 |
| C3×#463 | 3 |
| #4819 | 3 |