Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
326 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 35. C9×Dic6 | Q8 | semidirect |
| 153. C3×C9 | #477 | semidirect |
| 174. Dic6 | Dic18 | semidirect |
| 219. C9 | #5091 | semidirect |
| 248. C3 | #10588703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×Dic6 | 2 |
| C3×#63431 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720297 | 2 |
| #11720263 | 2 |
| #10590310 | 3 |
| #10588703 | 3 |