Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
306 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 119 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. C4×C9×3−1+2 | C2 | semidirect |
| 3. C9×3−1+2⋊C4 | C2 | semidirect |
| 6. C4×D9⋊C9 | C3 | semidirect |
| 7. C4×C9×D9 | C3 | semidirect |
| 9. C9×AGL(1,ℤ/9) | C4 | direct (N × H) |
| 19. C4×C9⋊C9 | C2×C3 | semidirect |
| 22. C4×C92 | C2×C3 | semidirect |
| 23. Dic9⋊C9 | C2×C3 | semidirect |
| 24. C9×Dic9 | C2×C3 | semidirect |
| 25. C9×3−1+2 | C2×C4 | semidirect |
| 28. C4×AGL(1,ℤ/9) | C9 | direct (N × H) |
| 41. D9⋊C9 | C3×C4 | semidirect |
| 42. C9×D9 | C3×C4 | semidirect |
| 52. C4×3−1+2 | C2×C9 | semidirect |
| 62. 3−1+2⋊C4 | C2×C9 | semidirect |
| 69. C9⋊C9 | C2×C3×C4 | semidirect |
| 72. C92 | C2×C3×C4 | semidirect |
| 78. C4×D9 | C3×C9 | semidirect |
| 92. AGL(1,ℤ/9) | C4×C9 | direct (N × H) |
| 117. C4×C9 | AGL(1,ℤ/9) | direct (N × H) |
| 118. C4×C9 | C2×C3×C9 | semidirect |
| 119. Dic9 | C2×C3×C9 | semidirect |
| 122. 3−1+2 | C2×C4×C9 | semidirect |
| 151. D9 | C3×C4×C9 | semidirect |
| 172. C9 | C4×AGL(1,ℤ/9) | direct (N × H) |
| 173. C9 | C2×C3×C4×C9 | semidirect |
| 184. C4 | C9×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×C9×AGL(1,ℤ/9) | 2 |
| C4×C9×3−1+2 | 2 |
| C9×3−1+2⋊C4 | 2 |
| C3×C4×AGL(1,ℤ/9) | 3 |
| C3×C4×D3×C9 | 3 |
| C4×D9⋊C9 | 3 |
| C4×C9×D9 | 3 |