Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
614 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 173 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×C3⋊(C3⋊Dic9) | C2 | semidirect |
| 3. C2×C9×C3⋊Dic3 | C2 | semidirect |
| 4. D9×C3⋊Dic3 | C2 | direct (N × H) |
| 8. C2×C32×D9 | C4 | semidirect |
| 10. C3⋊(C3⋊Dic9) | C22 | semidirect |
| 11. C9×C3⋊Dic3 | C22 | semidirect |
| 21. C2×C32×C9 | C2×C4 | semidirect |
| 23. C32×D9 | C2×C4 | semidirect |
| 34. C2×C3×D9 | Dic3 | semidirect |
| 39. C32×C9 | C22×C4 | semidirect |
| 46. C2×C3⋊Dic3 | D9 | direct (N × H) |
| 59. C2×C3×C9 | C2×Dic3 | semidirect |
| 61. C3×D9 | C2×Dic3 | semidirect |
| 74. C3⋊Dic3 | C2×D9 | direct (N × H) |
| 78. C2×D9 | C3⋊Dic3 | direct (N × H) |
| 85. C3×C9 | C22×Dic3 | semidirect |
| 98. C2×C32 | C4×D9 | semidirect |
| 105. C2×C9 | C2×C3⋊Dic3 | semidirect |
| 107. D9 | C2×C3⋊Dic3 | direct (N × H) |
| 122. C32 | C2×C4×D9 | semidirect |
| 125. C9 | C22×C3⋊Dic3 | semidirect |
| 133. C2×C3 | Dic3×D9 | semidirect |
| 144. C3 | C2×Dic3×D9 | semidirect |
| 147. C2 | D9×C3⋊Dic3 | 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×C3⋊(C3⋊Dic9) | 2 |
| C2×C9×C3⋊Dic3 | 2 |
| D9×C3⋊Dic3 | 2 |
| C2×D3×C3⋊Dic3 | 3 |
| C2×Dic3×D9 | 3 |