Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
660 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 224 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⋊(C3⋊Dic9) | C2 | semidirect |
| 3. C2×C3×C3⋊Dic9 | C2 | semidirect |
| 4. D3×C3⋊Dic9 | C2 | direct (N × H) |
| 9. C2×C3×D3×C9 | C4 | semidirect |
| 11. C3⋊(C3⋊Dic9) | C22 | semidirect |
| 12. C3×C3⋊Dic9 | C22 | semidirect |
| 24. C2×C3⋊Dic9 | D3 | direct (N × H) |
| 27. C2×C32×C9 | C2×C4 | semidirect |
| 29. C3×D3×C9 | C2×C4 | semidirect |
| 45. C2×D3×C9 | Dic3 | semidirect |
| 51. C3⋊Dic9 | C2×D3 | direct (N × H) |
| 53. C32×C9 | C22×C4 | semidirect |
| 81. C2×C3×C9 | C4×D3 | semidirect |
| 82. C2×C3×C9 | C2×Dic3 | semidirect |
| 85. D3×C9 | C2×Dic3 | semidirect |
| 96. C2×C3×D3 | Dic9 | semidirect |
| 118. C3×C9 | C2×C4×D3 | semidirect |
| 119. C3×C9 | C22×Dic3 | semidirect |
| 139. C2×C32 | C2×Dic9 | semidirect |
| 145. C3×D3 | C2×Dic9 | semidirect |
| 150. C2×C9 | D3×Dic3 | semidirect |
| 162. C2×D3 | C3⋊Dic9 | direct (N × H) |
| 174. C32 | C22×Dic9 | semidirect |
| 178. C9 | C2×D3×Dic3 | semidirect |
| 189. C2×C3 | D3×Dic9 | semidirect |
| 190. C2×C3 | C2×C3⋊Dic9 | semidirect |
| 195. D3 | C2×C3⋊Dic9 | direct (N × H) |
| 203. C3 | C2×D3×Dic9 | semidirect |
| 204. C3 | C22×C3⋊Dic9 | semidirect |
| 207. C2 | D3×C3⋊Dic9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D3×C9 | 2 |
| C2×C3⋊(C3⋊Dic9) | 2 |
| C2×C3×C3⋊Dic9 | 2 |
| D3×C3⋊Dic9 | 2 |
| C2×D3×C3⋊Dic3 | 3 |
| C22×C3⋊Dic9 | 3 |
| C2×D3×Dic9 | 3 |