Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
289 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 289 conjugacy classes of subgroups — too many to draw. Only its 84 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×D4×Dic3 | C2 | semidirect |
| 3. Dic3×D12 | C2 | semidirect |
| 4. #63659 | C2 | semidirect |
| 5. #63573 | C2 | semidirect |
| 6. #63562 | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 17. C3×#213 | C4 | semidirect |
| 25. D4×Dic3 | D3 | semidirect |
| 40. C32×D4 | C2×C4 | semidirect |
| 48. C3×D12 | C2×C4 | semidirect |
| 51. C3×C3⋊C8 | C2×C4 | semidirect |
| 69. #213 | Dic3 | semidirect |
| 111. C3×D4 | C4×D3 | semidirect |
| 112. C3×D4 | C2×Dic3 | semidirect |
| 129. D12 | C2×Dic3 | semidirect |
| 135. C3⋊C8 | C2×Dic3 | semidirect |
| 186. C32 | #442 | semidirect |
| 192. D4 | D3×Dic3 | semidirect |
| 230. C3 | #5014 | semidirect |
| 231. C3 | #5152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Dic3 | 2 |
| C2×C3×#213 | 2 |
| Dic3×D12 | 2 |
| #63659 | 2 |
| #63573 | 2 |
| #63562 | 2 |
| #63554 | 2 |
| #5152 | 3 |
| #5014 | 3 |