Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
437 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 437 conjugacy classes of subgroups — too many to draw. Only its 82 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. C3×C9×3−1+2 | C2 | semidirect |
| 4. C3⋊(D9⋊C9) | C3 | semidirect |
| 5. C9×C3⋊D9 | C3 | semidirect |
| 12. C9×3−1+2 | D3 | semidirect |
| 14. C3×C9⋊C9 | C2×C3 | semidirect |
| 17. C3×C92 | C2×C3 | semidirect |
| 19. C3⋊AGL(1,ℤ/9) | C9 | direct (N × H) |
| 32. C3×3−1+2 | C2×C9 | semidirect |
| 49. C9⋊C9 | C3×D3 | semidirect |
| 55. C92 | C3×D3 | semidirect |
| 61. C3⋊D9 | C3×C9 | semidirect |
| 78. 3−1+2 | D3×C9 | semidirect |
| 98. C3×C9 | AGL(1,ℤ/9) | semidirect |
| 99. C3×C9 | C2×C3×C9 | semidirect |
| 133. C9 | C3×D3×C9 | semidirect |
| 134. C9 | C3⋊AGL(1,ℤ/9) | direct (N × H) |
| 143. C3 | 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 |
|---|---|
| C3×C9×3−1+2 | 2 |
| C3×C3⋊AGL(1,ℤ/9) | 3 |
| C3×C9×C3⋊D3 | 3 |
| C3⋊(D9⋊C9) | 3 |
| C9×C3⋊D9 | 3 |
| C9×AGL(1,ℤ/9) | 3 |