Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
139 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 139 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. #10624792 | C2 | semidirect |
| 3. D9⋊H(3,𝔽3) | C3 | semidirect |
| 4. D9×H(3,𝔽3) | C3 | semidirect |
| 5. C3×D9⋊C9 | C3 | semidirect |
| 7. C9⋊H(3,𝔽3) | C2×C3 | semidirect |
| 8. C9×H(3,𝔽3) | C2×C3 | semidirect |
| 9. C3×C9⋊C9 | C2×C3 | semidirect |
| 56. H(3,𝔽3) | AGL(1,ℤ/9) | semidirect |
| 78. D9 | #732 | semidirect |
| 97. C9 | C2×#732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624792 | 2 |
| D3×#732 | 3 |
| D9⋊H(3,𝔽3) | 3 |
| D9×H(3,𝔽3) | 3 |
| C3×D9⋊C9 | 3 |