Finite Group DatabasebetaFinite Group Databasebeta← C4⋊(C3⋊((C3⋊D3)⋊C9)) #14517496
Order 1944.
489 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
| 12. C32×C4×C9 | D3 | semidirect |
| 15. C4×C32⋊C9 | D3 | semidirect |
| 16. C3×C32⋊C9 | D4 | semidirect |
| 17. C4⋊(C3⋊(C3⋊D3)) | C9 | semidirect |
| 31. C2×C3⋊(C3⋊D3) | C2×C9 | semidirect |
| 39. C33×C4 | C2×C9 | semidirect |
| 48. C3×C4×C9 | C3⋊D3 | semidirect |
| 51. C32×C9 | D12 | semidirect |
| 53. C32⋊C9 | D12 | semidirect |
| 94. C32×C4 | D3×C9 | semidirect |
| 105. C33 | D4×C9 | semidirect |
| 112. C3×C9 | C4⋊(C3⋊D3) | semidirect |
| 147. C3×C4 | (C3⋊D3)⋊C9 | semidirect |
| 159. C32 | C9×D12 | semidirect |
| 178. C4 | C3⋊((C3⋊D3)⋊C9) | semidirect |
| 183. C3 | C4⋊((C3⋊D3)⋊C9) | semidirect |
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 |
| C3×C4⋊(C3⋊(C3⋊D3)) | 3 |
| C9×C4⋊(C3⋊D3) | 3 |
| C4⋊((C3⋊D3)⋊C9) | 3 |