Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
272 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C2×C33 |
| prime radical | C2×C3×AΣL(1,𝔽27) | C3 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624801 | C2 | direct (N × H) |
| 3. C2×#6894 | C3 | semidirect |
| 4. C2×C9⋊H(3,𝔽3) | C3 | semidirect |
| 5. C2×C9×3−1+2 | C3 | semidirect |
| 6. C2×C3×C32⋊C9 | C3 | semidirect |
| 7. C2×3−1+2⋊C9 | C3 | semidirect |
| 8. C2×3−1+2⋊C9 | C3 | semidirect |
| 9. C2×3−1+2⋊C9 | C3 | semidirect |
| 10. C2×3−1+2⋊C9 | C3 | semidirect |
| 11. C2×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 12. C2×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 13. C2×#6866 | C3 | semidirect |
| 14. C2×#6866 | C3 | semidirect |
| 16. #6894 | C2×C3 | semidirect |
| 17. C9⋊H(3,𝔽3) | C2×C3 | semidirect |
| 18. C9×3−1+2 | C2×C3 | semidirect |
| 19. C3×C32⋊C9 | C2×C3 | semidirect |
| 20. 3−1+2⋊C9 | C2×C3 | semidirect |
| 21. 3−1+2⋊C9 | C2×C3 | semidirect |
| 22. 3−1+2⋊C9 | C2×C3 | semidirect |
| 23. 3−1+2⋊C9 | C2×C3 | semidirect |
| 24. H(3,𝔽3)⋊C9 | C2×C3 | semidirect |
| 25. H(3,𝔽3)⋊C9 | C2×C3 | semidirect |
| 26. #6866 | C2×C3 | semidirect |
| 27. #6866 | C2×C3 | semidirect |
| 92. C2×3−1+2 | 3−1+2 | semidirect |
| 123. 3−1+2 | C2×3−1+2 | semidirect |
| 216. C2 | #10624801 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624801 | 2 |
| C2×C3×AΣL(1,𝔽27) | 3 |
| C2×#6894 | 3 |
| C2×C9⋊H(3,𝔽3) | 3 |
| C2×C9×3−1+2 | 3 |
| C2×C3×C32⋊C9 | 3 |
| C2×3−1+2⋊C9 | 3 |
| C2×H(3,𝔽3)⋊C9 | 3 |
| C2×#6866 | 3 |