Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
562 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 103 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×C9×C3⋊Dic3 | C2 | semidirect |
| 3. C2×C32×Dic9 | C2 | semidirect |
| 9. C2×C3⋊(C3⋊D9) | C4 | semidirect |
| 18. C2×C3×Dic9 | D3 | semidirect |
| 42. C32×C9 | C22⋊C4 | semidirect |
| 47. C2×C3⋊Dic3 | D9 | semidirect |
| 53. C2×Dic9 | C3⋊D3 | semidirect |
| 96. C3×C9 | (C2×D3)⋊C4 | semidirect |
| 142. C32 | (C2×D9)⋊C4 | semidirect |
| 145. C9 | #3752 | semidirect |
| 168. C3 | #88445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊D9) | 2 |
| C2×C9×C3⋊Dic3 | 2 |
| C2×C32×Dic9 | 2 |
| #88804 | 3 |
| #88445 | 3 |