Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1052 conjugacy classes of subgroups.
The subgroup lattice has 364 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4⋊(C3⋊(C3⋊Dic3)) | C4 | semidirect |
| 13. C2×C3×C3⋊(C3⋊C8) | C4 | semidirect |
| 15. C32×C4⋊Dic3 | C4 | semidirect |
| 57. C2×C3⋊(C3⋊C8) | Dic3 | semidirect |
| 59. C3×C4⋊Dic3 | Dic3 | semidirect |
| 149. C4⋊Dic3 | C3⋊Dic3 | semidirect |
| 194. C33 | #340 | semidirect |
| 303. C32 | #4529 | semidirect |
| 304. C32 | #4551 | semidirect |
| 354. C3 | #10589164 | semidirect |
| 355. C3 | #10589395 | 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 |
| C22×C3×C3⋊(C3⋊C8) | 2 |
| C2×C32×C4⋊Dic3 | 2 |
| #10589395 | 3 |
| #10589164 | 3 |