Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
268 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×C3×Dic12 | C2 | semidirect |
| 4. C3×#869 | C2 | semidirect |
| 5. C32×#97 | C2 | semidirect |
| 7. #4715 | C3 | direct (N × H) |
| 21. C2×Dic12 | C2×C3 | semidirect |
| 24. #869 | C2×C3 | semidirect |
| 26. C3×#97 | D3 | semidirect |
| 27. C3×#97 | C2×C3 | semidirect |
| 70. #97 | C3×D3 | semidirect |
| 123. C32 | #497 | semidirect |
| 150. C3 | #4715 | direct (N × H) |
| 151. C3 | C3×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C2×C3×#204 | 2 |
| C3×#875 | 2 |
| C3×#869 | 2 |
| C32×#97 | 2 |
| C3×#497 | 3 |
| #4715 | 3 |