Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1532 conjugacy classes of subgroups.
The subgroup lattice has 362 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C4⋊(C3⋊(C3⋊Dic3)) | C4 | semidirect |
| 14. C3×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 15. C32×C4×Dic3 | C4 | semidirect |
| 62. C4⋊(C3⋊Dic3) | Dic3 | direct (N × H) |
| 65. C3×C4×Dic3 | Dic3 | semidirect |
| 74. C33×C4 | C42 | semidirect |
| 78. C32×Dic3 | C4⋊C4 | semidirect |
| 157. C4×Dic3 | C3⋊Dic3 | semidirect |
| 182. C32×C4 | C4×Dic3 | semidirect |
| 183. C32×C4 | C4×Dic3 | semidirect |
| 190. C3×Dic3 | C4⋊Dic3 | semidirect |
| 196. C33 | C4×C4⋊C4 | semidirect |
| 291. C3×C4 | Dic32 | semidirect |
| 292. C3×C4 | C4×C3⋊Dic3 | semidirect |
| 298. Dic3 | C4⋊(C3⋊Dic3) | direct (N × H) |
| 300. C32 | C4×C4⋊Dic3 | semidirect |
| 301. C32 | Dic3×C4⋊C4 | semidirect |
| 350. C4 | Dic3×C3⋊Dic3 | semidirect |
| 352. C3 | Dic3×C4⋊Dic3 | semidirect |
| 353. C3 | C4×C4⋊(C3⋊Dic3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×C3×C4⋊(C3⋊Dic3) | 2 |
| C2×C32×C4×Dic3 | 2 |
| C2×Dic3×C3⋊Dic3 | 2 |
| #11722061 | 2 |
| C4×C4⋊(C3⋊Dic3) | 3 |
| Dic3×C4⋊Dic3 | 3 |