Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
247 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 58 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. #64110 | C2 | semidirect |
| 2. C2×C3×D24 | C2 | semidirect |
| 3. #63830 | C2 | semidirect |
| 4. C3×#819 | C2 | semidirect |
| 5. #63558 | C2 | semidirect |
| 22. C2×D24 | D3 | semidirect |
| 29. #819 | D3 | semidirect |
| 148. C32 | #472 | semidirect |
| 180. C3 | #4897 | semidirect |
| 181. C3 | #5160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64110 | 2 |
| C2×C3×D24 | 2 |
| #63830 | 2 |
| C3×#819 | 2 |
| #63558 | 2 |
| #5160 | 3 |
| #4897 | 3 |