Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
742 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 210 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×C32×D9 | C2 | semidirect |
| 3. C32×#611 | C2 | direct (N × H) |
| 4. C2×C32×Dic9 | C2 | semidirect |
| 6. C2×C3×#611 | C3 | direct (N × H) |
| 9. C22×C32×C9 | C22 | semidirect |
| 11. C2×C32×D9 | C22 | semidirect |
| 12. C32×Dic9 | C22 | semidirect |
| 18. C23×C3×C9 | C2×C3 | semidirect |
| 19. C22×C3×D9 | C2×C3 | semidirect |
| 20. C3×#611 | C2×C3 | direct (N × H) |
| 21. C2×C3×Dic9 | C2×C3 | semidirect |
| 23. C2×C32×C9 | D4 | semidirect |
| 28. C2×#611 | C32 | direct (N × H) |
| 40. C22×C3×C9 | C22×C3 | semidirect |
| 42. C2×C3×D9 | C22×C3 | semidirect |
| 43. C3×Dic9 | C22×C3 | semidirect |
| 44. C32×C9 | C2×D4 | semidirect |
| 47. C23×C32 | D9 | semidirect |
| 55. C23×C9 | C2×C32 | semidirect |
| 56. C22×D9 | C2×C32 | semidirect |
| 57. #611 | C2×C32 | direct (N × H) |
| 58. C2×Dic9 | C2×C32 | semidirect |
| 67. C2×C3×C9 | C3×D4 | semidirect |
| 80. C22×C32 | C2×D9 | semidirect |
| 92. C22×C9 | C22×C32 | semidirect |
| 94. C2×D9 | C22×C32 | semidirect |
| 95. Dic9 | C22×C32 | semidirect |
| 98. C3×C9 | C2×C3×D4 | semidirect |
| 101. C23×C3 | C3×D9 | semidirect |
| 114. C2×C32 | #611 | direct (N × H) |
| 123. C2×C9 | C32×D4 | semidirect |
| 135. C22×C3 | C2×C3×D9 | semidirect |
| 143. C32 | C2×#611 | direct (N × H) |
| 146. C9 | C2×C32×D4 | semidirect |
| 148. C23 | C32×D9 | semidirect |
| 157. C2×C3 | C3×#611 | direct (N × H) |
| 166. C22 | C2×C32×D9 | semidirect |
| 169. C3 | C2×C3×#611 | direct (N × H) |
| 173. C2 | C32×#611 | 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×C32×D9 | 2 |
| C32×#611 | 2 |
| C2×C32×Dic9 | 2 |
| C2×C32×#67 | 3 |
| C2×C3×#611 | 3 |