Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
212 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 25 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. #10624761 | C2 | semidirect |
| 2. #92392 | C3 | semidirect |
| 3. #92283 | C3 | semidirect |
| 5. C3×#4174 | C3 | semidirect |
| 6. H(5,𝔽3) | C2×C3 | semidirect |
| 9. #6910 | C2×C3 | semidirect |
| 11. C3×AΣL(1,𝔽27) | D3 | semidirect |
| 12. C3×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 22. C34 | C3×D3 | semidirect |
| 25. C3×3−1+2 | C3×D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624761 | 2 |
| #92392 | 3 |
| #92283 | 3 |
| D3×AΣL(1,𝔽27) | 3 |
| C3×#4174 | 3 |