Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
515 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 515 conjugacy classes of subgroups — too many to draw. Only its 126 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×D3×C32⋊C9 | C2 | semidirect |
| 2. C3×C4×C32⋊C9 | C2 | semidirect |
| 4. C3×C9×D12 | C3 | semidirect |
| 10. C2×C3×D3×C9 | C2×C3 | semidirect |
| 11. C32×C4×C9 | C2×C3 | semidirect |
| 15. C4×C32⋊C9 | D3 | semidirect |
| 16. C3×C32⋊C9 | D4 | semidirect |
| 20. C32×D12 | C9 | semidirect |
| 35. C2×C32×D3 | C2×C9 | semidirect |
| 43. C33×C4 | C2×C9 | semidirect |
| 51. C3×C4×C9 | C3×D3 | semidirect |
| 53. C32×C9 | C3×D4 | semidirect |
| 56. C32⋊C9 | D12 | direct (N × H) |
| 106. C32×C4 | D3×C9 | semidirect |
| 120. C33 | D4×C9 | semidirect |
| 126. C3×C9 | C3×D12 | semidirect |
| 131. D12 | C32⋊C9 | direct (N × H) |
| 164. C2×D3 | C2×C32⋊C9 | semidirect |
| 170. C3×C4 | C2×C32⋊C9 | semidirect |
| 186. C32 | C9×D12 | semidirect |
| 209. C4 | D3×C32⋊C9 | semidirect |
| 215. C3 | D4×C32⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C32⋊C9 | 2 |
| C3×C4×C32⋊C9 | 2 |
| C33×D12 | 3 |
| C3×C9×D12 | 3 |
| D4×C32⋊C9 | 3 |