Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
307 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 307 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×C9⋊C9 | C2 | semidirect |
| 2. C22×D9⋊C9 | C2 | semidirect |
| 3. #611⋊C9 | C2 | direct (N × H) |
| 4. C2×Dic9⋊C9 | C2 | semidirect |
| 9. C22×C9⋊C9 | C22 | semidirect |
| 11. C2×D9⋊C9 | C22 | semidirect |
| 12. Dic9⋊C9 | C22 | semidirect |
| 23. C2×C9⋊C9 | D4 | semidirect |
| 28. C2×#611 | C9 | semidirect |
| 44. C9⋊C9 | C2×D4 | semidirect |
| 53. C23×C9 | C2×C9 | semidirect |
| 54. C22×D9 | C2×C9 | semidirect |
| 57. #611 | C2×C9 | semidirect |
| 58. C2×Dic9 | C2×C9 | semidirect |
| 91. C22×C9 | C22×C9 | semidirect |
| 93. C2×D9 | C22×C9 | semidirect |
| 95. Dic9 | C22×C9 | semidirect |
| 123. C2×C9 | D4×C9 | semidirect |
| 146. C9 | C2×D4×C9 | semidirect |
| 148. C23 | D9⋊C9 | semidirect |
| 166. C22 | C2×D9⋊C9 | semidirect |
| 173. C2 | #611⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C9⋊C9 | 2 |
| C22×D9⋊C9 | 2 |
| #611⋊C9 | 2 |
| C2×Dic9⋊C9 | 2 |
| C2×C9×#67 | 3 |
| C2×C3×#611 | 3 |