Finite Group DatabasebetaFinite Group Databasebeta← C3×(C3⋊D3)⋊(C22⋊C9) #14518212
Order 1944.
484 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 60 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 | semidirect |
| 4. (C3⋊D3)⋊(C22⋊C9) | C3 | direct (N × H) |
| 10. C32×C22⋊C9 | D3 | semidirect |
| 12. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 14. C22×C3×C3⋊D3 | C9 | semidirect |
| 30. C22×C33 | C2×C9 | semidirect |
| 46. C3×C22⋊C9 | C3×D3 | semidirect |
| 53. C22×C3⋊D3 | C3×C9 | semidirect |
| 69. C3×C3⋊D3 | C22⋊C9 | semidirect |
| 93. C22×C32 | C2×C3×C9 | semidirect |
| 112. C33 | C2×C22⋊C9 | semidirect |
| 144. C3⋊D3 | C3×C22⋊C9 | semidirect |
| 163. C22×C3 | (C3⋊D3)⋊C9 | semidirect |
| 184. C32 | C2×C3×C22⋊C9 | semidirect |
| 207. C22 | C3×(C3⋊D3)⋊C9 | semidirect |
| 213. C3 | (C3⋊D3)⋊(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 |
| C22×C32×C3⋊D3 | 3 |
| C3×D3×C22⋊C9 | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| C3×(C3⋊D3)⋊C9 | 4 |