Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
217 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 217 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. C2×Dic9⋊C9 | C2 | semidirect |
| 6. C22×C9⋊C9 | C4 | semidirect |
| 19. #3676 | C9 | semidirect |
| 31. C9⋊C9 | C22⋊C4 | semidirect |
| 39. C2×Dic9 | C2×C9 | semidirect |
| 65. C22×C9 | C4×C9 | semidirect |
| 108. C9 | C9×C22⋊C4 | semidirect |
| 121. C22 | Dic9⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C9⋊C9 | 2 |
| C2×Dic9⋊C9 | 2 |
| C9×#217 | 3 |
| C3×#3676 | 3 |