Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
213 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 3. #63643 | C2 | semidirect |
| 5. C3×#817 | C2 | semidirect |
| 6. #63575 | C2 | semidirect |
| 7. #63567 | C2 | semidirect |
| 29. #817 | D3 | semidirect |
| 167. C32 | #485 | semidirect |
| 204. C3 | #4723 | semidirect |
| 205. C3 | #4868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63857 | 2 |
| #63841 | 2 |
| #63643 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| C3×#817 | 2 |
| #63575 | 2 |
| #63567 | 2 |
| #4868 | 3 |
| #4723 | 3 |