Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1388 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 |
|---|---|---|
| 7. C3×#4984 | C3 | direct (N × H) |
| 13. C33×C4⋊C4 | C4 | semidirect |
| 45. #4984 | C32 | direct (N × H) |
| 61. C32×C4⋊C4 | Dic3 | semidirect |
| 62. C32×C4⋊C4 | C3×C4 | semidirect |
| 75. C33×C4 | C4⋊C4 | semidirect |
| 152. C3×C4⋊C4 | C3×Dic3 | semidirect |
| 153. C3×C4⋊C4 | C32×C4 | semidirect |
| 186. C32×C4 | C4⋊Dic3 | semidirect |
| 187. C32×C4 | C3×C4⋊C4 | semidirect |
| 196. C33 | #389 | semidirect |
| 264. C4⋊C4 | C32×Dic3 | semidirect |
| 294. C3×C4 | C3×C4⋊Dic3 | semidirect |
| 295. C3×C4 | C32×C4⋊C4 | semidirect |
| 300. C32 | #4984 | direct (N × H) |
| 301. C32 | C3×#389 | semidirect |
| 350. C4 | C32×C4⋊Dic3 | semidirect |
| 352. C3 | C3×#4984 | direct (N × H) |
| 353. C3 | C32×#389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C4⋊C4 | 2 |
| C2×C32×C4⋊Dic3 | 2 |
| C2×C32×C4×Dic3 | 2 |
| C32×C3⋊#95 | 2 |
| C32×#389 | 3 |
| C3×#4984 | 3 |