Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
500 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 270 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 |
|---|---|---|
| 3. C3×C9×Dic6 | C2 | direct (N × H) |
| 6. C2×C9×Dic6 | C3 | direct (N × H) |
| 20. C9×Dic6 | C2×C3 | direct (N × H) |
| 21. C2×C32×C9 | Q8 | semidirect |
| 24. C2×C3×Dic6 | C9 | direct (N × H) |
| 40. C32×C9 | C2×Q8 | semidirect |
| 50. C3×Dic6 | C2×C9 | direct (N × H) |
| 62. C2×C3×C9 | Dic6 | direct (N × H) |
| 63. C2×C3×C9 | C3×Q8 | semidirect |
| 68. C2×Dic6 | C3×C9 | direct (N × H) |
| 90. C3×C9 | C2×Dic6 | direct (N × H) |
| 91. C3×C9 | C2×C3×Q8 | semidirect |
| 102. Dic6 | C2×C3×C9 | direct (N × H) |
| 107. C2×C32 | Q8×C9 | semidirect |
| 115. C2×C9 | C3×Dic6 | direct (N × H) |
| 133. C32 | C2×Q8×C9 | semidirect |
| 137. C9 | C2×C3×Dic6 | direct (N × H) |
| 145. C2×C3 | C9×Dic6 | direct (N × H) |
| 146. C2×C3 | C3×Q8×C9 | semidirect |
| 156. C3 | C2×C9×Dic6 | direct (N × H) |
| 157. C3 | C2×C3×Q8×C9 | semidirect |
| 159. C2 | C3×C9×Dic6 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×C9 | 2 |
| C2×C3×C9×Dic3 | 2 |
| C3×C9×Dic6 | 2 |
| C2×C32×Dic6 | 3 |
| C2×C3×Q8×C9 | 3 |
| C2×C9×Dic6 | 3 |