Finite Group DatabasebetaFinite Group Databasebeta← C3×C4⋊((C3⋊D3)⋊C9) #14517284
Order 1944.
450 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×C3×(C3⋊D3)⋊C9 | C2 | semidirect |
| 2. C3×C4×C32⋊C9 | C2 | semidirect |
| 5. C4⋊((C3⋊D3)⋊C9) | C3 | direct (N × H) |
| 12. C32×C4×C9 | D3 | semidirect |
| 13. C2×(C3⋊D3)⋊C9 | C2×C3 | semidirect |
| 15. C4×C32⋊C9 | C2×C3 | semidirect |
| 16. C3×C32⋊C9 | D4 | semidirect |
| 17. C3×C4⋊(C3⋊D3) | C9 | semidirect |
| 31. C2×C3×C3⋊D3 | C2×C9 | semidirect |
| 40. C33×C4 | C2×C9 | semidirect |
| 50. C3×C4×C9 | C3×D3 | semidirect |
| 53. C32×C9 | D12 | semidirect |
| 55. C32⋊C9 | C3×D4 | semidirect |
| 57. C4⋊(C3⋊D3) | C3×C9 | semidirect |
| 84. C2×C3⋊D3 | C2×C3×C9 | semidirect |
| 103. C32×C4 | C2×C3×C9 | semidirect |
| 113. C33 | D4×C9 | semidirect |
| 121. C3×C9 | C3×D12 | semidirect |
| 160. C3×C4 | (C3⋊D3)⋊C9 | semidirect |
| 177. C32 | C3×D4×C9 | semidirect |
| 195. C4 | C3×(C3⋊D3)⋊C9 | semidirect |
| 201. C3 | C4⋊((C3⋊D3)⋊C9) | 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⋊D3)⋊C9 | 2 |
| C3×C4×C32⋊C9 | 2 |
| C32×C4⋊(C3⋊D3) | 3 |
| C3×C9×D12 | 3 |
| C4⋊((C3⋊D3)⋊C9) | 3 |