Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
283 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 283 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×(C3⋊Dic3)⋊C9 | C2 | semidirect |
| 6. C22×C32⋊C9 | C4 | semidirect |
| 17. #3757 | C9 | semidirect |
| 29. C22×C3×C9 | Dic3 | semidirect |
| 32. C32⋊C9 | C22⋊C4 | semidirect |
| 38. C2×C3⋊Dic3 | C2×C9 | semidirect |
| 67. C22×C32 | C4×C9 | semidirect |
| 83. C3×C9 | #217 | semidirect |
| 135. C32 | C9×C22⋊C4 | semidirect |
| 157. C22 | (C3⋊Dic3)⋊C9 | 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×(C3⋊Dic3)⋊C9 | 2 |
| C3×#3757 | 3 |
| C9×#217 | 3 |