Finite Group DatabasebetaFinite Group Databasebeta← C4×C3⋊((C3⋊D3)⋊C9) #14517494
Order 1944.
489 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C3×C4×C32⋊C9 | C2 | semidirect |
| 3. C3⋊((C3⋊Dic3)⋊C9) | C2 | semidirect |
| 8. C3⋊((C3⋊D3)⋊C9) | C4 | direct (N × H) |
| 14. C32×C4×C9 | D3 | semidirect |
| 18. C4×C32⋊C9 | D3 | semidirect |
| 20. C3×C32⋊C9 | C2×C4 | semidirect |
| 21. C4×C3⋊(C3⋊D3) | C9 | semidirect |
| 43. C33×C4 | C2×C9 | semidirect |
| 46. C3⋊(C3⋊Dic3) | C2×C9 | semidirect |
| 56. C3×C4×C9 | C3⋊D3 | semidirect |
| 61. C32×C9 | C4×D3 | semidirect |
| 63. C32⋊C9 | C4×D3 | semidirect |
| 78. C3⋊(C3⋊D3) | C4×C9 | semidirect |
| 104. C32×C4 | D3×C9 | semidirect |
| 122. C33 | C2×C4×C9 | semidirect |
| 129. C3×C9 | C4×C3⋊D3 | semidirect |
| 165. C3×C4 | (C3⋊D3)⋊C9 | semidirect |
| 180. C32 | C4×D3×C9 | semidirect |
| 200. C4 | C3⋊((C3⋊D3)⋊C9) | direct (N × H) |
| 205. 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⋊((C3⋊Dic3)⋊C9) | 2 |
| C3×C4×C3⋊(C3⋊D3) | 3 |
| C4×C9×C3⋊D3 | 3 |
| C4×(C3⋊D3)⋊C9 | 3 |