Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
319 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 86 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×#66316 | C2 | semidirect |
| 4. #88551 | C3 | semidirect |
| 6. C22×C32⋊C9 | C4 | semidirect |
| 13. C2×C3⋊Dic9 | C2×C3 | semidirect |
| 30. C22×C3×C9 | C3×C4 | semidirect |
| 33. C32⋊C9 | C22⋊C4 | semidirect |
| 70. C22×C32 | Dic9 | semidirect |
| 87. C3×C9 | C3×C22⋊C4 | semidirect |
| 141. C32 | #3676 | semidirect |
| 163. C22 | #66316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32⋊C9 | 2 |
| C2×#66316 | 2 |
| C3×#3757 | 3 |
| #88551 | 3 |