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. C3×#948 | C2 | semidirect |
| 3. #63817 | C2 | semidirect |
| 4. C3×#837 | C2 | semidirect |
| 5. #63578 | C2 | semidirect |
| 6. #63570 | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 12. #3756 | C4 | semidirect |
| 13. #3755 | C4 | semidirect |
| 14. #3754 | C4 | semidirect |
| 15. #3753 | C4 | semidirect |
| 29. #948 | D3 | semidirect |
| 33. #837 | D3 | semidirect |
| 194. C32 | #444 | semidirect |
| 232. C3 | #4823 | semidirect |
| 233. C3 | #5145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64159 | 2 |
| C3×#948 | 2 |
| #63817 | 2 |
| C3×#837 | 2 |
| #63578 | 2 |
| #63570 | 2 |
| #63554 | 2 |
| #5145 | 3 |
| #4823 | 3 |