Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
229 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
| 4. C3×#818 | C2 | semidirect |
| 5. C3×Dic3⋊C8 | C2 | semidirect |
| 6. #63573 | C2 | semidirect |
| 31. #818 | D3 | semidirect |
| 33. Dic3⋊C8 | D3 | semidirect |
| 166. C32 | #478 | semidirect |
| 203. C3 | #4847 | semidirect |
| 204. C3 | #4891 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63894 | 2 |
| #63869 | 2 |
| #63648 | 2 |
| C3×#818 | 2 |
| C3×Dic3⋊C8 | 2 |
| #63573 | 2 |
| #63564 | 2 |
| #4891 | 3 |
| #4847 | 3 |