Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
404 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 106 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. #6894⋊C2 | C3 | direct (N × H) |
| 5. C3×D9⋊C9 | C3 | semidirect |
| 9. #6894 | C2×C3 | semidirect |
| 11. C3×C9⋊C9 | C2×C3 | semidirect |
| 20. D9⋊C9 | C32 | semidirect |
| 36. C9⋊C9 | C2×C32 | semidirect |
| 46. C3×D9 | 3−1+2 | semidirect |
| 68. C3×C9 | C2×3−1+2 | semidirect |
| 78. D9 | C3×3−1+2 | semidirect |
| 96. C9 | C2×C3×3−1+2 | semidirect |
| 105. C3 | #6894⋊C2 | direct (N × H) |
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 |
| C33×D9 | 3 |
| #6894⋊C2 | 3 |
| C3×D9⋊C9 | 3 |