Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
742 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. C2×C9×C3⋊Dic3 | C2 | semidirect |
| 3. C2×C32×Dic9 | C2 | semidirect |
| 4. #10619870 | C2 | direct (N × H) |
| 8. C2×C3⋊(C3⋊D9) | C4 | semidirect |
| 10. C9×C3⋊Dic3 | C22 | semidirect |
| 11. C32×Dic9 | C22 | semidirect |
| 19. C2×C3×Dic9 | D3 | semidirect |
| 21. C2×C32×C9 | C2×C4 | semidirect |
| 23. C3⋊(C3⋊D9) | C2×C4 | semidirect |
| 39. C3×Dic9 | C2×D3 | semidirect |
| 40. C32×C9 | C22×C4 | semidirect |
| 45. C2×C3⋊Dic3 | D9 | semidirect |
| 53. C2×Dic9 | C3⋊D3 | semidirect |
| 60. C2×C3×C9 | C4×D3 | semidirect |
| 76. C3⋊Dic3 | C2×D9 | semidirect |
| 86. Dic9 | C2×C3⋊D3 | semidirect |
| 89. C3×C9 | C2×C4×D3 | semidirect |
| 101. C2×C32 | C4×D9 | semidirect |
| 110. C2×C9 | C4×C3⋊D3 | semidirect |
| 129. C32 | C2×C4×D9 | semidirect |
| 132. C9 | C2×C4×C3⋊D3 | semidirect |
| 139. C2×C3 | (C3⋊D9)⋊C4 | semidirect |
| 152. C3 | C2×(C3⋊D9)⋊C4 | semidirect |
| 155. C2 | #10619870 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C3⋊D9) | 2 |
| C2×C9×C3⋊Dic3 | 2 |
| C2×C32×Dic9 | 2 |
| #10619870 | 2 |
| C2×#6289 | 3 |
| C2×(C3⋊D9)⋊C4 | 3 |