Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
978 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 270 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×C32×AGL(1,ℤ/9) | C2 | semidirect |
| 2. C32×C4×3−1+2 | C2 | semidirect |
| 4. C3×C4⋊AGL(1,ℤ/9) | C3 | direct (N × H) |
| 5. C32×D36 | C3 | semidirect |
| 10. C2×C3×AGL(1,ℤ/9) | C2×C3 | semidirect |
| 11. C2×C32×D9 | C2×C3 | semidirect |
| 13. C3×C4×3−1+2 | C2×C3 | semidirect |
| 15. C32×C4×C9 | C2×C3 | semidirect |
| 16. C32×3−1+2 | D4 | semidirect |
| 20. C4⋊AGL(1,ℤ/9) | C32 | direct (N × H) |
| 21. C3×D36 | C32 | semidirect |
| 37. C2×AGL(1,ℤ/9) | C2×C32 | semidirect |
| 38. C2×C3×D9 | C2×C32 | semidirect |
| 40. C4×3−1+2 | C2×C32 | semidirect |
| 43. C3×C4×C9 | C2×C32 | semidirect |
| 46. C3×3−1+2 | C3×D4 | semidirect |
| 48. C32×C9 | C3×D4 | semidirect |
| 53. D36 | C33 | semidirect |
| 75. C32×C4 | AGL(1,ℤ/9) | semidirect |
| 78. C2×D9 | C2×C33 | semidirect |
| 81. C4×C9 | C2×C33 | semidirect |
| 87. 3−1+2 | C32×D4 | semidirect |
| 90. C3×C9 | C32×D4 | semidirect |
| 113. C3×C4 | C3×AGL(1,ℤ/9) | semidirect |
| 118. C32 | C4⋊AGL(1,ℤ/9) | direct (N × H) |
| 123. C9 | C33×D4 | semidirect |
| 133. C4 | C32×AGL(1,ℤ/9) | semidirect |
| 136. C3 | C3×C4⋊AGL(1,ℤ/9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×AGL(1,ℤ/9) | 2 |
| C32×C4×3−1+2 | 2 |
| C33×D12 | 3 |
| C3×C4⋊AGL(1,ℤ/9) | 3 |
| C32×D36 | 3 |