Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
225 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 60 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. #63918 | C2 | semidirect |
| 4. C3×#816 | C2 | semidirect |
| 5. C3×#815 | C2 | semidirect |
| 6. #63566 | C2 | semidirect |
| 33. #816 | D3 | semidirect |
| 34. #815 | D3 | semidirect |
| 172. C32 | #489 | semidirect |
| 211. C3 | #4714 | semidirect |
| 212. C3 | #4794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63918 | 2 |
| #63864 | 2 |
| #63648 | 2 |
| C3×#816 | 2 |
| C3×#815 | 2 |
| #63566 | 2 |
| #63564 | 2 |
| #4794 | 3 |
| #4714 | 3 |