Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2204 conjugacy classes of subgroups.
The subgroup lattice has 226 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#64157 | C2 | semidirect |
| 3. C2×C3×#3748 | C2 | semidirect |
| 4. #10596290 | C3 | direct (N × H) |
| 12. C3×#3748 | C22 | semidirect |
| 13. C2×C3×C3⋊(C3⋊C8) | C22 | semidirect |
| 17. #64157 | C2×C3 | semidirect |
| 18. C2×#3748 | C2×C3 | semidirect |
| 47. #3748 | C22×C3 | semidirect |
| 48. C2×C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 134. C33 | #568 | semidirect |
| 194. C32 | #5819 | semidirect |
| 195. C32 | C3×#568 | semidirect |
| 220. C3 | C3×#5819 | semidirect |
| 221. C3 | #10596290 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×#41 | 2 |
| C3×#64157 | 2 |
| C2×C3×#3748 | 2 |
| #10596290 | 3 |
| C3×#5819 | 3 |