Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
223 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 76 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. #63814 | C2 | semidirect |
| 3. #63646 | C2 | semidirect |
| 4. C3×#815 | C2 | semidirect |
| 5. #63569 | C2 | semidirect |
| 13. C3×Dic12 | C4 | semidirect |
| 14. C3×D24 | C4 | semidirect |
| 15. C3×#204 | C4 | semidirect |
| 27. #815 | D3 | semidirect |
| 57. Dic12 | Dic3 | semidirect |
| 58. D24 | Dic3 | semidirect |
| 59. #204 | Dic3 | semidirect |
| 125. C32 | #444 | semidirect |
| 151. C3 | #4717 | semidirect |
| 152. C3 | #5197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#904 | 2 |
| #63814 | 2 |
| #63646 | 2 |
| C3×#815 | 2 |
| #63569 | 2 |
| #5197 | 3 |
| #4717 | 3 |