Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
243 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×#837 | C2 | semidirect |
| 4. C3×#819 | C2 | semidirect |
| 5. C3×C8×Dic3 | C2 | semidirect |
| 7. #5196 | C3 | direct (N × H) |
| 9. C32×Q16 | C4 | semidirect |
| 10. C32×SD16 | C4 | semidirect |
| 11. C32×D8 | C4 | semidirect |
| 22. #948 | C2×C3 | semidirect |
| 26. #837 | C2×C3 | semidirect |
| 27. #819 | C2×C3 | semidirect |
| 28. C8×Dic3 | C2×C3 | semidirect |
| 45. C3×Q16 | Dic3 | semidirect |
| 46. C3×Q16 | C3×C4 | semidirect |
| 48. C3×SD16 | Dic3 | semidirect |
| 49. C3×SD16 | C3×C4 | semidirect |
| 51. C3×D8 | Dic3 | semidirect |
| 52. C3×D8 | C3×C4 | semidirect |
| 110. Q16 | C3×Dic3 | semidirect |
| 111. SD16 | C3×Dic3 | semidirect |
| 112. D8 | C3×Dic3 | semidirect |
| 136. C32 | #443 | semidirect |
| 164. C3 | #5196 | direct (N × H) |
| 165. C3 | C3×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#135 | 2 |
| C3×#948 | 2 |
| C3×#837 | 2 |
| C3×#819 | 2 |
| C3×C8×Dic3 | 2 |
| C3×#443 | 3 |
| #5196 | 3 |