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. C32×#948 | C2 | semidirect |
| 3. C2×C32×#208 | C2 | semidirect |
| 5. C3×#5819 | C3 | direct (N × H) |
| 12. C32×#208 | C22 | semidirect |
| 13. C2×C32×C3⋊C8 | C22 | semidirect |
| 19. C3×#948 | C2×C3 | semidirect |
| 20. C2×C3×#208 | C2×C3 | semidirect |
| 30. #5819 | C32 | direct (N × H) |
| 50. C3×#208 | C22×C3 | semidirect |
| 51. C2×C3×C3⋊C8 | C22×C3 | semidirect |
| 63. #948 | C2×C32 | semidirect |
| 64. C2×#208 | C2×C32 | semidirect |
| 111. #208 | C22×C32 | semidirect |
| 112. C2×C3⋊C8 | C22×C32 | semidirect |
| 134. C33 | #568 | semidirect |
| 194. C32 | #5819 | direct (N × H) |
| 195. C32 | C3×#568 | semidirect |
| 220. C3 | C3×#5819 | direct (N × H) |
| 221. C3 | C32×#568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×#41 | 2 |
| C32×#948 | 2 |
| C2×C32×#208 | 2 |
| C32×#568 | 3 |
| C3×#5819 | 3 |