Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
353 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 353 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×#6894 | C2 | semidirect |
| 4. C3⋊(D9⋊C9) | C3 | semidirect |
| 10. #6894 | D3 | semidirect |
| 12. C3×C9⋊C9 | C2×C3 | semidirect |
| 40. C9⋊C9 | C3×D3 | semidirect |
| 48. C3⋊D9 | 3−1+2 | semidirect |
| 79. C3×C9 | C2×3−1+2 | semidirect |
| 111. C9 | D3×3−1+2 | semidirect |
| 121. C3 | #6894⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6894 | 2 |
| C3⋊D3×3−1+2 | 3 |
| C32×C3⋊D9 | 3 |
| C3⋊(D9⋊C9) | 3 |
| #6894⋊C2 | 3 |