Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
241 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 241 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 |
|---|---|---|
| 4. C2×#3719 | C2 | semidirect |
| 5. #63643 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. #63573 | C2 | semidirect |
| 36. #816 | D3 | semidirect |
| 181. C32 | #470 | semidirect |
| 220. C3 | #4816 | semidirect |
| 221. C3 | #5137 | 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 |
| #63857 | 2 |
| #63856 | 2 |
| C2×#3719 | 2 |
| #63643 | 2 |
| C3×#816 | 2 |
| #63573 | 2 |
| #5137 | 3 |
| #4816 | 3 |