Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
227 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 227 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×#907 | C2 | semidirect |
| 3. C32×#108 | C2 | semidirect |
| 4. C3×#825 | C2 | semidirect |
| 5. C3×C8×Dic3 | C2 | semidirect |
| 7. #4895 | C3 | direct (N × H) |
| 13. C3×Dic12 | C4 | semidirect |
| 14. C3×D24 | C4 | semidirect |
| 15. C3×#204 | C4 | semidirect |
| 20. #907 | C2×C3 | semidirect |
| 23. C3×#108 | D3 | semidirect |
| 24. C3×#108 | C2×C3 | semidirect |
| 27. #825 | C2×C3 | semidirect |
| 28. C8×Dic3 | C2×C3 | semidirect |
| 58. Dic12 | C3×C4 | semidirect |
| 59. D24 | C3×C4 | semidirect |
| 60. #204 | C3×C4 | semidirect |
| 71. #108 | C3×D3 | semidirect |
| 128. C32 | #443 | semidirect |
| 155. C3 | #4895 | direct (N × H) |
| 156. C3 | C3×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#907 | 2 |
| C3×#904 | 2 |
| C32×#108 | 2 |
| C3×#825 | 2 |
| C3×C8×Dic3 | 2 |
| C3×#443 | 3 |
| #4895 | 3 |