Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
302 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. C4⋊(C3⋊Dic9) | C2 | semidirect |
| 4. C3×C4⋊Dic9 | C2 | semidirect |
| 5. Dic3⋊Dic9 | C2 | semidirect |
| 13. C4×D3×C9 | C4 | semidirect |
| 25. C4⋊Dic9 | D3 | direct (N × H) |
| 30. C3×C4×C9 | C2×C4 | semidirect |
| 32. C9×Dic3 | C2×C4 | semidirect |
| 55. D3×C9 | C4⋊C4 | semidirect |
| 82. C4×C9 | C4×D3 | semidirect |
| 87. C3×C9 | C2×C4⋊C4 | semidirect |
| 103. C4×D3 | Dic9 | semidirect |
| 132. C3×C4 | C2×Dic9 | semidirect |
| 138. Dic3 | C2×Dic9 | semidirect |
| 141. C9 | D3×C4⋊C4 | semidirect |
| 159. D3 | C4⋊Dic9 | direct (N × H) |
| 167. C4 | D3×Dic9 | semidirect |
| 169. C3 | C2×C4⋊Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C9 | 2 |
| C2×D3×Dic9 | 2 |
| C4⋊(C3⋊Dic9) | 2 |
| C3×C4⋊Dic9 | 2 |
| Dic3⋊Dic9 | 2 |
| D3×C4⋊Dic3 | 3 |
| C2×C4⋊Dic9 | 3 |