Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
434 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 136 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. C3×C4×C3⋊Dic3 | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 4. C3×Dic3⋊Dic3 | C2 | semidirect |
| 8. #63855 | C3 | direct (N × H) |
| 14. C32×C4×D3 | C4 | semidirect |
| 20. C4×C3⋊Dic3 | C2×C3 | semidirect |
| 29. C3×C4×Dic3 | D3 | semidirect |
| 30. C3×C4×Dic3 | C2×C3 | semidirect |
| 31. Dic3⋊Dic3 | C2×C3 | semidirect |
| 68. C3×C4×D3 | Dic3 | semidirect |
| 69. C3×C4×D3 | C3×C4 | semidirect |
| 90. C4×Dic3 | C3×D3 | semidirect |
| 126. C33 | #117 | semidirect |
| 153. C4×D3 | C3×Dic3 | semidirect |
| 215. C32 | #872 | semidirect |
| 216. C32 | #926 | semidirect |
| 217. C32 | C3×#117 | semidirect |
| 253. C3 | #63855 | direct (N × H) |
| 254. C3 | C3×#872 | semidirect |
| 255. C3 | C3×#926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D3 | 2 |
| C3×C4×C3⋊Dic3 | 2 |
| C32×C4×Dic3 | 2 |
| C3×Dic3⋊Dic3 | 2 |
| C3×(C2×D3)⋊Dic3 | 2 |
| C3×#926 | 3 |
| C3×#872 | 3 |
| #63855 | 3 |