Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
265 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 64 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×ΓL(1,𝔽25) | C2 | semidirect |
| 3. #63856 | C2 | semidirect |
| 4. C2×#3717 | C2 | semidirect |
| 5. #63648 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. #63575 | C2 | semidirect |
| 29. C2×ΓL(1,𝔽25) | D3 | semidirect |
| 36. #816 | D3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 141. C3⋊C8 | #67 | semidirect |
| 193. C32 | #468 | semidirect |
| 238. C3 | #4812 | semidirect |
| 239. C3 | #5134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×ΓL(1,𝔽25) | 2 |
| #63909 | 2 |
| #63856 | 2 |
| C2×#3717 | 2 |
| #63648 | 2 |
| C3×#816 | 2 |
| #63575 | 2 |
| #5134 | 3 |
| #4812 | 3 |