Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
380 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 9. C3×C3⋊Dic9 | C4 | semidirect |
| 42. C3⋊Dic9 | Dic3 | semidirect |
| 45. C32×C9 | C4⋊C4 | semidirect |
| 104. C3×C9 | Dic3⋊C4 | semidirect |
| 105. C3×C9 | C4⋊Dic3 | semidirect |
| 157. C32 | Dic9⋊C4 | semidirect |
| 161. C9 | Dic3⋊Dic3 | semidirect |
| 186. C3 | Dic9⋊Dic3 | semidirect |
| 187. C3 | #88534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊Dic9) | 2 |
| C2×C3×C3⋊Dic9 | 2 |
| C2×C3×C9×Dic3 | 2 |
| #88807 | 3 |
| #88534 | 3 |
| Dic9⋊Dic3 | 3 |