Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
545 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 545 conjugacy classes of subgroups — too many to draw. Only its 107 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×#4181 | C2 | semidirect |
| 3. #10619675 | C2 | direct (N × H) |
| 4. C2×#66328 | C2 | semidirect |
| 9. C22×C32⋊C9 | C22 | semidirect |
| 11. C2×#4181 | C22 | semidirect |
| 12. #66328 | C22 | semidirect |
| 17. C23×C3×C9 | D3 | semidirect |
| 22. C2×C32⋊C9 | D4 | semidirect |
| 37. C22×C3×C9 | C2×D3 | semidirect |
| 41. C32⋊C9 | C2×D4 | semidirect |
| 44. C23×C32 | D9 | semidirect |
| 64. C2×C3×C9 | #67 | semidirect |
| 79. C22×C32 | C2×D9 | semidirect |
| 98. C3×C9 | C2×#67 | semidirect |
| 120. C2×C32 | #611 | semidirect |
| 155. C32 | C2×#611 | semidirect |
| 159. C23 | #4181 | semidirect |
| 181. C22 | C2×#4181 | semidirect |
| 189. C2 | #10619675 | 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×#4181 | 2 |
| #10619675 | 2 |
| C2×#66328 | 2 |
| C2×C3×#638 | 3 |
| C2×C3×#611 | 3 |