Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
414 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#3748 | C2 | semidirect |
| 3. C3×#926 | C2 | semidirect |
| 4. #63562 | C2 | semidirect |
| 11. C2×C3×D12 | C4 | semidirect |
| 14. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 16. C3×C4⋊Dic3 | C22 | semidirect |
| 21. #926 | D3 | semidirect |
| 52. C2×D12 | Dic3 | semidirect |
| 58. C4⋊Dic3 | C2×D3 | semidirect |
| 153. C32 | #418 | semidirect |
| 189. C3 | #5001 | semidirect |
| 190. C3 | #5215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D12 | 2 |
| C2×#3748 | 2 |
| C3×#926 | 2 |
| #63562 | 2 |
| #5215 | 3 |
| #5001 | 3 |