Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
258 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 258 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×C3×#204 | C2 | semidirect |
| 2. C2×C3×ΓL(1,𝔽25) | C2 | semidirect |
| 4. #63856 | C2 | semidirect |
| 5. #63645 | C2 | semidirect |
| 6. #63566 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 29. C2×#204 | D3 | semidirect |
| 30. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 52. C32×C8 | D4 | semidirect |
| 137. C3×C8 | #67 | semidirect |
| 138. C3×C8 | #67 | semidirect |
| 189. C32 | #468 | semidirect |
| 205. C8 | #625 | semidirect |
| 233. C3 | #5134 | semidirect |
| 234. C3 | #5174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#204 | 2 |
| C2×C3×ΓL(1,𝔽25) | 2 |
| #63908 | 2 |
| #63856 | 2 |
| #63645 | 2 |
| #63566 | 2 |
| #63563 | 2 |
| #5174 | 3 |
| #5134 | 3 |