Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
614 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 614 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. C22×C32×D9 | C2 | semidirect |
| 2. C2×C32×C4×C9 | C2 | semidirect |
| 3. C32×D36 | C2 | direct (N × H) |
| 5. C2×C3×D36 | C3 | direct (N × H) |
| 8. C2×C32×D9 | C22 | semidirect |
| 9. C32×C4×C9 | C22 | semidirect |
| 13. C22×C3×D9 | C2×C3 | semidirect |
| 15. C2×C3×C4×C9 | C2×C3 | semidirect |
| 16. C3×D36 | C2×C3 | direct (N × H) |
| 17. C2×C32×C9 | D4 | semidirect |
| 22. C2×D36 | C32 | direct (N × H) |
| 30. C2×C3×D9 | C22×C3 | semidirect |
| 32. C3×C4×C9 | C22×C3 | semidirect |
| 33. C32×C9 | C2×D4 | semidirect |
| 38. C2×C32×C4 | D9 | semidirect |
| 41. C22×D9 | C2×C32 | semidirect |
| 43. C2×C4×C9 | C2×C32 | semidirect |
| 44. D36 | C2×C32 | direct (N × H) |
| 50. C2×C3×C9 | C3×D4 | semidirect |
| 63. C32×C4 | C2×D9 | semidirect |
| 68. C2×D9 | C22×C32 | semidirect |
| 70. C4×C9 | C22×C32 | semidirect |
| 73. C3×C9 | C2×C3×D4 | semidirect |
| 78. C2×C3×C4 | C3×D9 | semidirect |
| 84. C2×C32 | D36 | direct (N × H) |
| 91. C2×C9 | C32×D4 | semidirect |
| 103. C3×C4 | C2×C3×D9 | semidirect |
| 106. C32 | C2×D36 | direct (N × H) |
| 109. C9 | C2×C32×D4 | semidirect |
| 112. C2×C4 | C32×D9 | semidirect |
| 116. C2×C3 | C3×D36 | direct (N × H) |
| 124. C4 | C2×C32×D9 | semidirect |
| 126. C3 | C2×C3×D36 | direct (N × H) |
| 129. C2 | C32×D36 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D9 | 2 |
| C2×C32×C4×C9 | 2 |
| C32×D36 | 2 |
| C2×C32×D12 | 3 |
| C2×C3×D36 | 3 |