Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1490 conjugacy classes of subgroups.
The subgroup lattice has 222 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C9×C4⋊Dic3 | C2 | direct (N × H) |
| 7. C22×C3×C4×C9 | C4 | semidirect |
| 11. C9×C4⋊Dic3 | C22 | direct (N × H) |
| 23. C2×C3×C4×C9 | C2×C4 | semidirect |
| 28. C22×C4⋊Dic3 | C9 | direct (N × H) |
| 41. C22×C4×C9 | Dic3 | semidirect |
| 44. C22×C3×C9 | C4⋊C4 | semidirect |
| 49. C3×C4×C9 | C22×C4 | semidirect |
| 57. C2×C4⋊Dic3 | C2×C9 | direct (N × H) |
| 78. C2×C4×C9 | C2×Dic3 | semidirect |
| 81. C2×C3×C9 | C2×C4⋊C4 | semidirect |
| 92. C22×C3×C4 | C4×C9 | semidirect |
| 99. C4⋊Dic3 | C22×C9 | direct (N × H) |
| 112. C22×C9 | C4⋊Dic3 | direct (N × H) |
| 119. C4×C9 | C22×Dic3 | semidirect |
| 123. C3×C9 | C22×C4⋊C4 | semidirect |
| 140. C2×C3×C4 | C2×C4×C9 | semidirect |
| 154. C2×C9 | C2×C4⋊Dic3 | direct (N × H) |
| 161. C22×C4 | C9×Dic3 | semidirect |
| 169. C22×C3 | C9×C4⋊C4 | semidirect |
| 181. C3×C4 | C22×C4×C9 | semidirect |
| 186. C9 | C22×C4⋊Dic3 | direct (N × H) |
| 193. C2×C4 | C2×C9×Dic3 | semidirect |
| 199. C2×C3 | C2×C9×C4⋊C4 | semidirect |
| 207. C22 | C9×C4⋊Dic3 | direct (N × H) |
| 213. C4 | C22×C9×Dic3 | semidirect |
| 215. C3 | C22×C9×C4⋊C4 | semidirect |
| 217. C2 | C2×C9×C4⋊Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4×C9 | 2 |
| C23×C9×Dic3 | 2 |
| C2×C9×C4⋊Dic3 | 2 |
| C22×C3×C4⋊Dic3 | 3 |
| C22×C9×C4⋊C4 | 3 |