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 |
| 12. C3×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 15. C2×C32×C3⋊C8 | C4 | semidirect |
| 57. C4⋊(C3⋊Dic3) | Dic3 | semidirect |
| 62. C2×C3×C3⋊C8 | Dic3 | semidirect |
| 152. C2×C3⋊C8 | C3⋊Dic3 | semidirect |
| 194. C33 | #340 | semidirect |
| 303. C32 | #4529 | semidirect |
| 304. C32 | #4551 | semidirect |
| 354. C3 | #10589164 | semidirect |
| 355. C3 | #10589417 | 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 |
| C22×C32×C3⋊C8 | 2 |
| #10589417 | 3 |
| #10589164 | 3 |