Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
506 conjugacy classes of subgroups.
The subgroup lattice has 346 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11720299 | C2 | direct (N × H) |
| 141. C2×C3×C9 | #101 | semidirect |
| 205. C3×C9 | C2×#101 | semidirect |
| 256. C2×C9 | #824 | semidirect |
| 300. C9 | C2×#824 | semidirect |
| 325. C2×C3 | #63394 | semidirect |
| 339. C3 | C2×#63394 | semidirect |
| 343. C2 | #11720299 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Dic6 | 2 |
| C2×#88532 | 2 |
| C2×C3×#3667 | 2 |
| #11720299 | 2 |
| C2×#63560 | 3 |
| C2×#63394 | 3 |