Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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×C9×Dic3 | C4 | semidirect |
| 10. C9×#217 | C4 | semidirect |
| 30. #4472 | C9 | direct (N × H) |
| 95. C22×Dic3 | C4×C9 | semidirect |
| 104. #217 | C4×C9 | semidirect |
| 135. C3×C9 | #352 | semidirect |
| 205. C9 | #4472 | direct (N × H) |
| 237. C3 | C9×#352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#935 | 2 |
| C3×C9×#99 | 2 |
| C9×#833 | 2 |
| C3×#4472 | 3 |
| C9×#352 | 3 |