Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
298 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 298 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×#3745 | C2 | semidirect |
| 2. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 3. #63909 | C2 | semidirect |
| 4. C3×#817 | C2 | semidirect |
| 5. #63564 | C2 | semidirect |
| 22. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 26. #817 | D3 | semidirect |
| 38. C32×C8 | D4 | semidirect |
| 103. C3×C8 | D12 | semidirect |
| 104. C3×C8 | #67 | semidirect |
| 145. C32 | #469 | semidirect |
| 157. C8 | #626 | semidirect |
| 180. C3 | #4865 | semidirect |
| 181. C3 | #5135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| #63909 | 2 |
| C3×#817 | 2 |
| #63564 | 2 |
| #5135 | 3 |
| #4865 | 3 |