Finite Group DatabasebetaFinite Group Databasebeta← C2×C3×C32⋊(C22⋊C9) #14518449
Order 1944.
1424 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 244 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. C3×C32⋊(C22⋊C9) | C2 | direct (N × H) |
| 3. C2×C32×C22⋊C9 | C3 | semidirect |
| 4. C2×C32⋊(C22⋊C9) | C3 | direct (N × H) |
| 9. C32×C22⋊C9 | C2×C3 | semidirect |
| 10. C32⋊(C22⋊C9) | C2×C3 | direct (N × H) |
| 14. C23×C33 | C9 | semidirect |
| 18. C2×C3×C22⋊C9 | C32 | semidirect |
| 36. C22×C33 | C2×C9 | semidirect |
| 40. C3×C22⋊C9 | C2×C32 | semidirect |
| 48. C23×C32 | C3×C9 | semidirect |
| 65. C2×C33 | C22⋊C9 | semidirect |
| 90. C22×C32 | C2×C3×C9 | semidirect |
| 97. C33 | C2×C22⋊C9 | semidirect |
| 103. C23×C3 | C32⋊C9 | semidirect |
| 127. C2×C32 | C3×C22⋊C9 | semidirect |
| 143. C22×C3 | C2×C32⋊C9 | semidirect |
| 151. C32 | C2×C3×C22⋊C9 | semidirect |
| 156. C23 | C3×C32⋊C9 | semidirect |
| 168. C2×C3 | C32⋊(C22⋊C9) | direct (N × H) |
| 174. C22 | C2×C3×C32⋊C9 | semidirect |
| 176. C3 | C2×C32⋊(C22⋊C9) | direct (N × H) |
| 182. C2 | C3×C32⋊(C22⋊C9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊(C22⋊C9) | 2 |
| C23×C34 | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×C3×C32⋊C9 | 4 |