Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
393 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C23×C32⋊C9 | C2 | semidirect |
| 2. C22×(C3⋊D3)⋊C9 | C2 | semidirect |
| 3. #638⋊C9 | C2 | direct (N × H) |
| 4. C2×(C3⋊Dic3)⋊C9 | C2 | semidirect |
| 9. C22×C32⋊C9 | C22 | semidirect |
| 11. C2×(C3⋊D3)⋊C9 | C22 | semidirect |
| 12. (C3⋊Dic3)⋊C9 | C22 | semidirect |
| 18. C23×C3×C9 | D3 | semidirect |
| 23. C2×C32⋊C9 | D4 | semidirect |
| 26. C2×#638 | C9 | semidirect |
| 41. C22×C3×C9 | C2×D3 | semidirect |
| 45. C32⋊C9 | C2×D4 | semidirect |
| 49. C23×C32 | C2×C9 | semidirect |
| 51. C22×C3⋊D3 | C2×C9 | semidirect |
| 54. #638 | C2×C9 | semidirect |
| 55. C2×C3⋊Dic3 | C2×C9 | semidirect |
| 73. C2×C3×C9 | #67 | semidirect |
| 91. C22×C32 | C22×C9 | semidirect |
| 95. C2×C3⋊D3 | C22×C9 | semidirect |
| 100. C3⋊Dic3 | C22×C9 | semidirect |
| 114. C3×C9 | C2×#67 | semidirect |
| 140. C2×C32 | D4×C9 | semidirect |
| 182. C32 | C2×D4×C9 | semidirect |
| 187. C23 | (C3⋊D3)⋊C9 | semidirect |
| 212. C22 | C2×(C3⋊D3)⋊C9 | semidirect |
| 221. C2 | #638⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32⋊C9 | 2 |
| C22×(C3⋊D3)⋊C9 | 2 |
| #638⋊C9 | 2 |
| C2×(C3⋊Dic3)⋊C9 | 2 |
| C2×C3×#638 | 3 |
| C2×C9×#67 | 3 |