Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
500 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. #10619868 | C2 | direct (N × H) |
| 26. C2×C32×C9 | Q8 | semidirect |
| 48. C32×C9 | C2×Q8 | semidirect |
| 74. C2×C3×C9 | Dic6 | semidirect |
| 75. C2×C3×C9 | Dic6 | semidirect |
| 106. C3×C9 | C2×Dic6 | semidirect |
| 107. C3×C9 | C2×Dic6 | semidirect |
| 126. C2×C32 | Dic18 | semidirect |
| 134. C2×C9 | #627 | semidirect |
| 155. C32 | C2×Dic18 | semidirect |
| 159. C9 | C2×#627 | semidirect |
| 168. C2×C3 | #6189 | semidirect |
| 169. C2×C3 | #6226 | semidirect |
| 180. C3 | C2×#6189 | semidirect |
| 181. C3 | C2×#6226 | semidirect |
| 183. C2 | #10619868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C3⋊Dic9) | 2 |
| C2×C3×C3⋊Dic9 | 2 |
| C2×C3×C9×Dic3 | 2 |
| #10619868 | 2 |
| C2×#6293 | 3 |
| C2×#6226 | 3 |
| C2×#6189 | 3 |