Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
245 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 245 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 |
|---|---|---|
| 2. #63869 | C2 | semidirect |
| 3. #63648 | C2 | semidirect |
| 4. C3×#821 | C2 | semidirect |
| 5. C3×#815 | C2 | semidirect |
| 6. #63564 | C2 | semidirect |
| 7. #63563 | C2 | semidirect |
| 33. #821 | D3 | semidirect |
| 34. #815 | D3 | semidirect |
| 182. C32 | #490 | semidirect |
| 226. C3 | #4713 | semidirect |
| 227. C3 | #4764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63911 | 2 |
| #63869 | 2 |
| #63648 | 2 |
| C3×#821 | 2 |
| C3×#815 | 2 |
| #63564 | 2 |
| #63563 | 2 |
| #4764 | 3 |
| #4713 | 3 |