Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 32. C3×C8×C9 | Q8 | semidirect |
| 33. C3×C9⋊C8 | Q8 | semidirect |
| 87. C8×C9 | Dic6 | semidirect |
| 88. C9⋊C8 | Dic6 | semidirect |
| 132. C3×C9 | #500 | semidirect |
| 149. C3×C8 | Dic18 | semidirect |
| 188. C9 | #4682 | semidirect |
| 196. C8 | #6189 | semidirect |
| 214. C3 | #10588554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720969 | 2 |
| #11720541 | 2 |
| C9×#818 | 2 |
| C3×C8×Dic9 | 2 |
| #11720262 | 2 |
| #10590891 | 3 |
| #10588554 | 3 |