Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
984 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 210 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×C9×C3⋊D3 | C2 | semidirect |
| 2. C33×C4×C9 | C2 | semidirect |
| 4. C9×C4⋊(C3⋊D3) | C3 | direct (N × H) |
| 10. C2×C9×C3⋊D3 | C2×C3 | semidirect |
| 14. C32×C4×C9 | D3 | semidirect |
| 15. C32×C4×C9 | C2×C3 | semidirect |
| 16. C33×C9 | D4 | semidirect |
| 17. C3×C4⋊(C3⋊D3) | C9 | direct (N × H) |
| 30. C2×C3×C3⋊D3 | C2×C9 | semidirect |
| 35. C33×C4 | C2×C9 | semidirect |
| 44. C3×C4×C9 | C3×D3 | semidirect |
| 45. C3×C4×C9 | C3⋊D3 | semidirect |
| 49. C32×C9 | D12 | semidirect |
| 50. C32×C9 | C3×D4 | semidirect |
| 52. C4⋊(C3⋊D3) | C3×C9 | direct (N × H) |
| 73. C2×C3⋊D3 | C2×C3×C9 | semidirect |
| 81. C32×C4 | D3×C9 | semidirect |
| 82. C32×C4 | C2×C3×C9 | semidirect |
| 87. C4×C9 | C3×C3⋊D3 | semidirect |
| 90. C33 | D4×C9 | semidirect |
| 97. C3×C9 | C3×D12 | semidirect |
| 98. C3×C9 | C4⋊(C3⋊D3) | direct (N × H) |
| 123. C3×C4 | C3×D3×C9 | semidirect |
| 124. C3×C4 | C9×C3⋊D3 | semidirect |
| 131. C32 | C9×D12 | semidirect |
| 132. C32 | C3×D4×C9 | semidirect |
| 136. C9 | C3×C4⋊(C3⋊D3) | direct (N × H) |
| 147. C4 | C3×C9×C3⋊D3 | semidirect |
| 150. C3 | C3×C9×D12 | semidirect |
| 151. C3 | C9×C4⋊(C3⋊D3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×C3⋊D3 | 2 |
| C33×C4×C9 | 2 |
| C32×C4⋊(C3⋊D3) | 3 |
| C9×C4⋊(C3⋊D3) | 3 |
| C3×C9×D12 | 3 |