Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
231 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 70 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×#214 | C2 | semidirect |
| 3. C3×#909 | C2 | semidirect |
| 4. C3×#907 | C2 | semidirect |
| 5. C32×#100 | C2 | semidirect |
| 6. C3×#824 | C2 | semidirect |
| 7. C3×#822 | C2 | semidirect |
| 9. #4748 | C3 | direct (N × H) |
| 29. C2×#214 | C2×C3 | semidirect |
| 31. #909 | C2×C3 | semidirect |
| 32. #907 | C2×C3 | semidirect |
| 36. C3×#100 | D3 | semidirect |
| 37. C3×#100 | C2×C3 | semidirect |
| 38. #824 | C2×C3 | semidirect |
| 39. #822 | C2×C3 | semidirect |
| 104. #100 | C3×D3 | semidirect |
| 183. C32 | #471 | semidirect |
| 220. C3 | #4748 | direct (N × H) |
| 221. C3 | C3×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#214 | 2 |
| C3×#932 | 2 |
| C3×#909 | 2 |
| C3×#907 | 2 |
| C32×#100 | 2 |
| C3×#824 | 2 |
| C3×#822 | 2 |
| C3×#471 | 3 |
| #4748 | 3 |