Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
261 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 68 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. #63918 | C2 | semidirect |
| 3. #63659 | C2 | semidirect |
| 4. C3×#832 | C2 | semidirect |
| 5. #63563 | C2 | semidirect |
| 6. #63562 | C2 | semidirect |
| 7. Dic3×C3⋊C8 | C2 | semidirect |
| 31. #832 | D3 | semidirect |
| 185. C32 | #486 | semidirect |
| 230. C3 | #4760 | semidirect |
| 231. C3 | #5070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#940 | 2 |
| #63918 | 2 |
| #63659 | 2 |
| C3×#832 | 2 |
| #63563 | 2 |
| #63562 | 2 |
| Dic3×C3⋊C8 | 2 |
| #5070 | 3 |
| #4760 | 3 |