Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
250 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 250 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 |
| 11. C9×#217 | C4 | semidirect |
| 30. #4476 | C9 | direct (N × H) |
| 95. C22×Dic3 | C4×C9 | semidirect |
| 105. #217 | C4×C9 | semidirect |
| 134. C3×C9 | #352 | semidirect |
| 203. C9 | #4476 | direct (N × H) |
| 235. 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×#100 | 2 |
| C9×#834 | 2 |
| C3×#4476 | 3 |
| C9×#352 | 3 |