Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3276 conjugacy classes of subgroups.
The subgroup lattice has 260 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C33×C4⋊C4 | C2 | semidirect |
| 4. C2×C4⋊(C3⋊(C3⋊Dic3)) | C2 | semidirect |
| 5. #11722201 | C2 | semidirect |
| 14. C2×C4×C3⋊(C3⋊D3) | C4 | semidirect |
| 19. C2×C32×C4⋊C4 | D3 | semidirect |
| 69. C2×C3⋊(C3⋊D3) | C4⋊C4 | semidirect |
| 71. C33×C4 | C22⋊C4 | semidirect |
| 75. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 135. C32×C4 | (C2×D3)⋊C4 | semidirect |
| 140. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 143. C33 | #380 | semidirect |
| 199. C3×C4 | #3752 | semidirect |
| 202. C32 | #4987 | semidirect |
| 249. C4 | #88859 | semidirect |
| 250. C3 | #10592686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊(C3⋊D3) | 2 |
| C2×C33×C4⋊C4 | 2 |
| C2×#88859 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #11722201 | 2 |
| #10592686 | 3 |