Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
742 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 177 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×C9×C3⋊D3 | C2 | semidirect |
| 3. C9×#638 | C2 | direct (N × H) |
| 4. C2×C9×C3⋊Dic3 | C2 | semidirect |
| 9. C22×C32×C9 | C22 | semidirect |
| 11. C2×C9×C3⋊D3 | C22 | semidirect |
| 12. C9×C3⋊Dic3 | C22 | semidirect |
| 18. C23×C3×C9 | D3 | semidirect |
| 23. C2×C32×C9 | D4 | semidirect |
| 26. C2×#638 | C9 | direct (N × H) |
| 40. C22×C3×C9 | C2×D3 | semidirect |
| 44. C32×C9 | C2×D4 | semidirect |
| 46. C23×C32 | C2×C9 | semidirect |
| 48. C22×C3⋊D3 | C2×C9 | semidirect |
| 50. #638 | C2×C9 | direct (N × H) |
| 51. C2×C3⋊Dic3 | C2×C9 | semidirect |
| 56. C23×C9 | C3⋊D3 | semidirect |
| 67. C2×C3×C9 | #67 | semidirect |
| 78. C22×C32 | C22×C9 | semidirect |
| 82. C2×C3⋊D3 | C22×C9 | semidirect |
| 85. C3⋊Dic3 | C22×C9 | semidirect |
| 94. C22×C9 | C2×C3⋊D3 | semidirect |
| 98. C3×C9 | C2×#67 | semidirect |
| 101. C23×C3 | D3×C9 | semidirect |
| 113. C2×C32 | D4×C9 | semidirect |
| 124. C2×C9 | #638 | direct (N × H) |
| 135. C22×C3 | C2×D3×C9 | semidirect |
| 143. C32 | C2×D4×C9 | semidirect |
| 146. C9 | C2×#638 | direct (N × H) |
| 148. C23 | C9×C3⋊D3 | semidirect |
| 157. C2×C3 | C9×#67 | semidirect |
| 166. C22 | C2×C9×C3⋊D3 | semidirect |
| 169. C3 | C2×C9×#67 | semidirect |
| 173. C2 | C9×#638 | 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×C9×C3⋊D3 | 2 |
| C9×#638 | 2 |
| C2×C9×C3⋊Dic3 | 2 |
| C2×C3×#638 | 3 |
| C2×C9×#67 | 3 |