Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
341 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 61 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×#6896 | C2 | semidirect |
| 4. C3⋊(D9⋊C9) | C3 | semidirect |
| 5. C9×C3⋊D9 | C3 | semidirect |
| 12. #6896 | D3 | semidirect |
| 15. C3×C9⋊C9 | C2×C3 | semidirect |
| 17. C3×C92 | C2×C3 | semidirect |
| 51. C9⋊C9 | C3×D3 | semidirect |
| 55. C92 | C3×D3 | semidirect |
| 61. C3⋊D9 | 3−1+2 | semidirect |
| 98. C3×C9 | AGL(1,ℤ/9) | semidirect |
| 99. C3×C9 | C2×3−1+2 | semidirect |
| 133. C9 | D3×3−1+2 | semidirect |
| 134. C9 | C3⋊AGL(1,ℤ/9) | semidirect |
| 143. C3 | #92264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6896 | 2 |
| C3⋊D3×3−1+2 | 3 |
| C3×C3⋊AGL(1,ℤ/9) | 3 |
| C3⋊(D9⋊C9) | 3 |
| C9×C3⋊D9 | 3 |
| #92264 | 3 |