Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3452 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×C32×C4⋊Dic3 | C2 | direct (N × H) |
| 5. C22×C3×C4⋊Dic3 | C3 | direct (N × H) |
| 7. C22×C33×C4 | C4 | semidirect |
| 11. C32×C4⋊Dic3 | C22 | direct (N × H) |
| 18. C2×C3×C4⋊Dic3 | C2×C3 | direct (N × H) |
| 23. C2×C33×C4 | C2×C4 | semidirect |
| 28. C22×C4⋊Dic3 | C32 | direct (N × H) |
| 36. C22×C32×C4 | Dic3 | semidirect |
| 37. C22×C32×C4 | C3×C4 | semidirect |
| 43. C3×C4⋊Dic3 | C22×C3 | direct (N × H) |
| 44. C22×C33 | C4⋊C4 | semidirect |
| 49. C33×C4 | C22×C4 | semidirect |
| 57. C2×C4⋊Dic3 | C2×C32 | direct (N × H) |
| 74. C2×C32×C4 | C2×Dic3 | semidirect |
| 75. C2×C32×C4 | C2×C3×C4 | semidirect |
| 81. C2×C33 | C2×C4⋊C4 | semidirect |
| 92. C22×C3×C4 | C3×Dic3 | semidirect |
| 93. C22×C3×C4 | C32×C4 | semidirect |
| 99. C4⋊Dic3 | C22×C32 | direct (N × H) |
| 105. C22×C32 | C4⋊Dic3 | direct (N × H) |
| 106. C22×C32 | C3×C4⋊C4 | semidirect |
| 117. C32×C4 | C22×Dic3 | semidirect |
| 118. C32×C4 | C22×C3×C4 | semidirect |
| 123. C33 | C22×C4⋊C4 | semidirect |
| 140. C2×C3×C4 | C2×C3×Dic3 | semidirect |
| 141. C2×C3×C4 | C2×C32×C4 | semidirect |
| 150. C2×C32 | C2×C4⋊Dic3 | direct (N × H) |
| 151. C2×C32 | C2×C3×C4⋊C4 | semidirect |
| 161. C22×C4 | C32×Dic3 | semidirect |
| 169. C22×C3 | C3×C4⋊Dic3 | direct (N × H) |
| 170. C22×C3 | C32×C4⋊C4 | semidirect |
| 181. C3×C4 | C22×C3×Dic3 | semidirect |
| 182. C3×C4 | C22×C32×C4 | semidirect |
| 185. C32 | C22×C4⋊Dic3 | direct (N × H) |
| 186. C32 | C22×C3×C4⋊C4 | semidirect |
| 193. C2×C4 | C2×C32×Dic3 | semidirect |
| 199. C2×C3 | C2×C3×C4⋊Dic3 | direct (N × H) |
| 200. C2×C3 | C2×C32×C4⋊C4 | semidirect |
| 207. C22 | C32×C4⋊Dic3 | direct (N × H) |
| 213. C4 | C22×C32×Dic3 | semidirect |
| 215. C3 | C22×C3×C4⋊Dic3 | direct (N × H) |
| 216. C3 | C22×C32×C4⋊C4 | semidirect |
| 217. C2 | C2×C32×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×C33×C4 | 2 |
| C23×C32×Dic3 | 2 |
| C2×C32×C4⋊Dic3 | 2 |
| C22×C32×C4⋊C4 | 3 |
| C22×C3×C4⋊Dic3 | 3 |