Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
418 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 190 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. C32×C4⋊Q8 | C2 | semidirect |
| 3. C3×Q8×Dic3 | C2 | semidirect |
| 5. C3×#889 | C2 | semidirect |
| 7. C3×#870 | C2 | semidirect |
| 9. #5731 | C3 | direct (N × H) |
| 24. C3×C4⋊Q8 | D3 | semidirect |
| 25. C3×C4⋊Q8 | C2×C3 | semidirect |
| 33. Q8×Dic3 | C2×C3 | semidirect |
| 35. #889 | C2×C3 | semidirect |
| 37. #870 | C2×C3 | semidirect |
| 86. C4⋊Q8 | C3×D3 | semidirect |
| 153. C32 | #541 | semidirect |
| 181. C3 | #5731 | direct (N × H) |
| 182. C3 | C3×#541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4⋊Q8 | 2 |
| C3×#946 | 2 |
| C3×Q8×Dic3 | 2 |
| C3×#898 | 2 |
| C3×#889 | 2 |
| C3×#872 | 2 |
| C3×#870 | 2 |
| C3×#541 | 3 |
| #5731 | 3 |