Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
274 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 68 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×#3744 | C2 | semidirect |
| 2. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 4. #63857 | C2 | semidirect |
| 5. C3×#818 | C2 | semidirect |
| 6. #63567 | C2 | semidirect |
| 7. #63564 | C2 | semidirect |
| 29. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 34. #818 | D3 | semidirect |
| 52. C32×C8 | D4 | semidirect |
| 142. C3×C8 | D12 | semidirect |
| 143. C3×C8 | #67 | semidirect |
| 196. C32 | #468 | semidirect |
| 212. C8 | #626 | semidirect |
| 241. C3 | #4886 | semidirect |
| 242. C3 | #5134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3744 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| #63909 | 2 |
| #63857 | 2 |
| C3×#818 | 2 |
| #63567 | 2 |
| #63564 | 2 |
| #5134 | 3 |
| #4886 | 3 |