Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
183 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 28 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. #10624794 | C2 | semidirect |
| 2. C32×AGL(1,ℤ/9) | C3 | semidirect |
| 4. #6894⋊C2 | C3 | semidirect |
| 5. D9×H(3,𝔽3) | C3 | semidirect |
| 6. C32×3−1+2 | C2×C3 | semidirect |
| 8. #6894 | C2×C3 | semidirect |
| 9. C9×H(3,𝔽3) | C2×C3 | semidirect |
| 66. H(3,𝔽3) | AGL(1,ℤ/9) | semidirect |
| 87. D9 | AΣL(1,𝔽27) | semidirect |
| 108. C9 | C2×AΣL(1,𝔽27) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624794 | 2 |
| C32×AGL(1,ℤ/9) | 3 |
| D3×AΣL(1,𝔽27) | 3 |
| #6894⋊C2 | 3 |
| D9×H(3,𝔽3) | 3 |