Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C22×C3×C4×C9 | C4 | semidirect |
| 10. C3×C9×C22⋊C4 | C4 | semidirect |
| 30. #4539 | C9 | direct (N × H) |
| 41. C22×C4×C9 | Dic3 | semidirect |
| 49. C9×C22⋊C4 | Dic3 | semidirect |
| 100. C22×C3×C4 | C4×C9 | semidirect |
| 111. C3×C22⋊C4 | C4×C9 | semidirect |
| 144. C3×C9 | #352 | semidirect |
| 183. C22×C4 | C9×Dic3 | semidirect |
| 188. C22⋊C4 | C9×Dic3 | semidirect |
| 217. C9 | #4539 | direct (N × H) |
| 249. C3 | C9×#352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#123 | 2 |
| C9×#834 | 2 |
| C9×#833 | 2 |
| C3×#4539 | 3 |
| C9×#352 | 3 |