Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
261 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 74 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. #63844 | C2 | semidirect |
| 4. #63643 | C2 | semidirect |
| 6. C3×#815 | C2 | semidirect |
| 7. #63575 | C2 | semidirect |
| 21. #3716 | C4 | semidirect |
| 35. #815 | D3 | semidirect |
| 42. #634 | C2×C4 | semidirect |
| 50. C3×C3⋊C8 | C2×C4 | semidirect |
| 130. C3⋊C8 | C4×D3 | semidirect |
| 174. C32 | #440 | semidirect |
| 212. C3 | #4710 | semidirect |
| 213. C3 | #4757 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×D12 | 2 |
| #63844 | 2 |
| C2×#3716 | 2 |
| #63643 | 2 |
| C3×#821 | 2 |
| C3×#815 | 2 |
| #63575 | 2 |
| #4757 | 3 |
| #4710 | 3 |