Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
273 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×C3×#204 | C2 | semidirect |
| 2. Dic3×D12 | C2 | semidirect |
| 3. #63864 | C2 | semidirect |
| 5. #63648 | C2 | semidirect |
| 6. C3×Dic3⋊C8 | C2 | semidirect |
| 7. #63566 | C2 | semidirect |
| 28. C2×#204 | D3 | semidirect |
| 37. Dic3⋊C8 | D3 | semidirect |
| 193. C32 | #463 | semidirect |
| 238. C3 | #4844 | semidirect |
| 239. C3 | #5165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#204 | 2 |
| Dic3×D12 | 2 |
| #63864 | 2 |
| C2×#3714 | 2 |
| #63648 | 2 |
| C3×Dic3⋊C8 | 2 |
| #63566 | 2 |
| #5165 | 3 |
| #4844 | 3 |