Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
222 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 222 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 |
|---|---|---|
| 2. #63869 | C2 | semidirect |
| 3. #63644 | C2 | semidirect |
| 5. C3×Dic3⋊C8 | C2 | semidirect |
| 6. #63575 | C2 | semidirect |
| 34. Dic3⋊C8 | D3 | semidirect |
| 162. C32 | #478 | semidirect |
| 198. C3 | #4763 | semidirect |
| 199. C3 | #4847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×D12 | 2 |
| #63869 | 2 |
| #63644 | 2 |
| C3×#821 | 2 |
| C3×Dic3⋊C8 | 2 |
| #63575 | 2 |
| #63563 | 2 |
| #4847 | 3 |
| #4763 | 3 |