Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
239 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 239 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. #63817 | C2 | semidirect |
| 3. C3×#819 | C2 | semidirect |
| 4. C3×#815 | C2 | semidirect |
| 5. #63570 | C2 | semidirect |
| 10. #3746 | C4 | semidirect |
| 11. #3745 | C4 | semidirect |
| 12. #3744 | C4 | semidirect |
| 26. #819 | D3 | semidirect |
| 27. #815 | D3 | semidirect |
| 133. C32 | #444 | semidirect |
| 160. C3 | #4717 | semidirect |
| 161. C3 | #4894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64113 | 2 |
| #63817 | 2 |
| C3×#819 | 2 |
| C3×#815 | 2 |
| #63570 | 2 |
| #4894 | 3 |
| #4717 | 3 |