Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
326 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 36. C3×Dic18 | Q8 | semidirect |
| 100. Dic18 | Dic6 | semidirect |
| 153. C3×C9 | #475 | semidirect |
| 219. C9 | #5020 | semidirect |
| 248. C3 | #10588767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#869 | 2 |
| C3×C4×Dic18 | 2 |
| C4⋊(C3⋊(C9⋊C8)) | 2 |
| #11720268 | 2 |
| #11720265 | 2 |
| #10590285 | 3 |
| #10588767 | 3 |