Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
354 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 88 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×#634 | C2 | semidirect |
| 3. C32×#208 | C2 | semidirect |
| 4. C3×#3719 | C2 | semidirect |
| 5. C3×#3716 | C2 | semidirect |
| 8. #63831 | C3 | direct (N × H) |
| 19. C2×#634 | C2×C3 | semidirect |
| 30. C3×#208 | D3 | semidirect |
| 31. C3×#208 | C2×C3 | semidirect |
| 34. #3719 | C2×C3 | semidirect |
| 35. #3716 | C2×C3 | semidirect |
| 102. #208 | C3×D3 | semidirect |
| 139. C33 | #137 | semidirect |
| 239. C32 | #909 | semidirect |
| 240. C32 | #951 | semidirect |
| 241. C32 | C3×#137 | semidirect |
| 279. C3 | #63831 | direct (N × H) |
| 280. C3 | C3×#909 | semidirect |
| 281. C3 | C3×#951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#634 | 2 |
| C32×#235 | 2 |
| C32×#208 | 2 |
| C3×#3719 | 2 |
| C3×#3716 | 2 |
| C3×#951 | 3 |
| C3×#909 | 3 |
| #63831 | 3 |