Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
306 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 99 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×C9×AGL(1,ℤ/9) | C2 | semidirect |
| 2. C4×C9×3−1+2 | C2 | semidirect |
| 5. C4⋊(D9⋊C9) | C3 | semidirect |
| 6. C9×D36 | C3 | semidirect |
| 13. C2×D9⋊C9 | C2×C3 | semidirect |
| 14. C2×C9×D9 | C2×C3 | semidirect |
| 16. C4×C9⋊C9 | C2×C3 | semidirect |
| 19. C4×C92 | C2×C3 | semidirect |
| 20. C9×3−1+2 | D4 | semidirect |
| 23. C4⋊AGL(1,ℤ/9) | C9 | direct (N × H) |
| 41. C2×AGL(1,ℤ/9) | C2×C9 | semidirect |
| 46. C4×3−1+2 | C2×C9 | semidirect |
| 58. C9⋊C9 | C3×D4 | semidirect |
| 61. C92 | C3×D4 | semidirect |
| 67. D36 | C3×C9 | semidirect |
| 94. C2×D9 | C2×C3×C9 | semidirect |
| 101. C4×C9 | AGL(1,ℤ/9) | semidirect |
| 102. C4×C9 | C2×C3×C9 | semidirect |
| 105. 3−1+2 | D4×C9 | semidirect |
| 152. C9 | C4⋊AGL(1,ℤ/9) | direct (N × H) |
| 153. C9 | C3×D4×C9 | semidirect |
| 163. C4 | C9×AGL(1,ℤ/9) | semidirect |
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 |
| C3×C4⋊AGL(1,ℤ/9) | 3 |
| C3×C9×D12 | 3 |
| C4⋊(D9⋊C9) | 3 |
| C9×D36 | 3 |