Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
470 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 250 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. C32×Q8×C9 | C2 | semidirect |
| 3. C3×C9×Dic6 | C2 | semidirect |
| 6. D3×Q8×C9 | C3 | direct (N × H) |
| 16. C3×Q8×C9 | D3 | direct (N × H) |
| 17. C3×Q8×C9 | C2×C3 | semidirect |
| 20. C9×Dic6 | C2×C3 | semidirect |
| 22. C3×D3×C9 | Q8 | direct (N × H) |
| 24. C3×D3×Q8 | C9 | direct (N × H) |
| 38. C32×C9 | C2×Q8 | semidirect |
| 42. C32×Q8 | C2×C9 | semidirect |
| 48. C3×Dic6 | C2×C9 | semidirect |
| 52. Q8×C9 | C3×D3 | direct (N × H) |
| 61. D3×C9 | C3×Q8 | direct (N × H) |
| 64. D3×Q8 | C3×C9 | direct (N × H) |
| 83. C3×C9 | D3×Q8 | direct (N × H) |
| 84. C3×C9 | C2×C3×Q8 | semidirect |
| 89. C3×Q8 | D3×C9 | direct (N × H) |
| 90. C3×Q8 | C2×C3×C9 | semidirect |
| 95. Dic6 | C2×C3×C9 | semidirect |
| 102. C3×D3 | Q8×C9 | direct (N × H) |
| 121. C32 | C2×Q8×C9 | semidirect |
| 125. C9 | C3×D3×Q8 | direct (N × H) |
| 127. Q8 | C3×D3×C9 | direct (N × H) |
| 136. D3 | C3×Q8×C9 | direct (N × H) |
| 142. C3 | D3×Q8×C9 | direct (N × H) |
| 143. C3 | C2×C3×Q8×C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 2 |
| C3×C4×D3×C9 | 2 |
| C3×C9×Dic6 | 2 |
| C32×D3×Q8 | 3 |
| C2×C3×Q8×C9 | 3 |
| D3×Q8×C9 | 3 |