Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
249 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×C3×#216 | C2 | semidirect |
| 5. C32×#103 | C2 | semidirect |
| 6. C3×#816 | C2 | semidirect |
| 7. C3×#807 | C2 | semidirect |
| 9. #4813 | C3 | direct (N × H) |
| 28. C2×#216 | C2×C3 | semidirect |
| 34. C3×#103 | D3 | semidirect |
| 35. C3×#103 | C2×C3 | semidirect |
| 36. #816 | C2×C3 | semidirect |
| 37. #807 | C2×C3 | semidirect |
| 86. C2×C3×D3 | Q16 | semidirect |
| 100. #103 | C3×D3 | semidirect |
| 162. C2×D3 | C3×Q16 | semidirect |
| 181. C32 | #467 | semidirect |
| 220. C3 | #4813 | direct (N × H) |
| 221. C3 | C3×#467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#946 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×D3×C8 | 2 |
| C3×#897 | 2 |
| C32×#103 | 2 |
| C3×#816 | 2 |
| C3×#807 | 2 |
| C3×#467 | 3 |
| #4813 | 3 |