Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. C2×#3743 | C2 | semidirect |
| 2. C2×C3×#204 | C2 | semidirect |
| 4. #63871 | C2 | semidirect |
| 5. C3×#818 | C2 | semidirect |
| 6. #63565 | C2 | semidirect |
| 7. #63562 | C2 | semidirect |
| 26. C2×#204 | D3 | semidirect |
| 35. #818 | D3 | semidirect |
| 52. C32×C8 | D4 | semidirect |
| 139. C3×C8 | D12 | semidirect |
| 140. C3×C8 | #67 | semidirect |
| 195. C32 | #468 | semidirect |
| 211. C8 | #626 | semidirect |
| 240. C3 | #4886 | semidirect |
| 241. C3 | #5174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| C2×C3×#204 | 2 |
| #63916 | 2 |
| #63871 | 2 |
| C3×#818 | 2 |
| #63565 | 2 |
| #63562 | 2 |
| #5174 | 3 |
| #4886 | 3 |