Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
833 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 833 conjugacy classes of subgroups — too many to draw. Only its 281 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 | direct (N × H) |
| 5. C22×C32⋊C9 | C22 | semidirect |
| 6. C2×(C3⋊D3)⋊C9 | C22 | direct (N × H) |
| 10. C23×C3×C9 | D3 | semidirect |
| 12. C2×C32⋊C9 | C23 | semidirect |
| 13. (C3⋊D3)⋊C9 | C23 | direct (N × H) |
| 14. C23×C3⋊D3 | C9 | semidirect |
| 21. C22×C3×C9 | C2×D3 | semidirect |
| 23. C32⋊C9 | C24 | semidirect |
| 27. C23×C32 | C2×C9 | semidirect |
| 29. C22×C3⋊D3 | C2×C9 | semidirect |
| 38. C2×C3×C9 | C22×D3 | semidirect |
| 46. C22×C32 | C22×C9 | semidirect |
| 48. C2×C3⋊D3 | C22×C9 | semidirect |
| 56. C3×C9 | C23×D3 | semidirect |
| 68. C2×C32 | C23×C9 | semidirect |
| 70. C3⋊D3 | C23×C9 | semidirect |
| 88. C32 | C24×C9 | semidirect |
| 93. C23 | (C3⋊D3)⋊C9 | direct (N × H) |
| 103. C22 | C2×(C3⋊D3)⋊C9 | direct (N × H) |
| 110. C2 | C22×(C3⋊D3)⋊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 |
| C23×C3×C3⋊D3 | 3 |
| C23×D3×C9 | 3 |