Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
5490 conjugacy classes of subgroups; only the 2878 normal subgroups are shown.
This group has 5490 conjugacy classes of subgroups — too many to draw. Only its 2878 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C34×C19⋊C3 |
| commutator, socle, cosocle | C3×C19 | C35 |
| Fitting | C19×3−1+4 | C3 |
| prime radical | C19⋊H(5,𝔽3) | C3 |
| hypercenter | 3−1+4 | C19⋊C3 |
| hypocenter | C19 | #10624943 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ 3−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17987547 | C3 | semidirect |
| 2. #17987546 | C3 | semidirect |
| 3. #17987545 | C3 | semidirect |
| 4. #17987544 | C3 | semidirect |
| 6. C3×#13095333 | C3 | semidirect |
| 7. C3×#13095331 | C3 | semidirect |
| 8. C19⋊C3×#737 | C3 | semidirect |
| 9. C19×3−1+4 | C3 | semidirect |
| 10. #13095333 | C32 | semidirect |
| 11. #13095333 | C32 | semidirect |
| 12. #13095333 | C32 | semidirect |
| 13. #13095333 | C32 | semidirect |
| 14. #13095333 | C32 | semidirect |
| 15. #13095333 | C32 | semidirect |
| 16. #13095332 | C32 | semidirect |
| 17. #13095331 | C32 | semidirect |
| 18. #13095331 | C32 | semidirect |
| 19. #13095331 | C32 | semidirect |
| 20. #13095331 | C32 | semidirect |
| 21. C3×#10587025 | C32 | semidirect |
| 22. C3×#10587025 | C32 | semidirect |
| 23. C3×#10587022 | C32 | semidirect |
| 24. C3×#10587023 | C32 | semidirect |
| 25. 3−1+2×C19⋊C3 | C32 | semidirect |
| 28. C32×#4294 | C32 | semidirect |
| 29. C3×C9×C19⋊C3 | C32 | semidirect |
| 30. C19×#737 | C32 | semidirect |
| 31. C3×C19×3−1+2 | C32 | semidirect |
| 61. 3−1+4 | C19⋊C3 | semidirect |
| 88. #737 | C3×C19⋊C3 | semidirect |
| 94. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 127. C19 | #10624943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987547 | 3 |
| #17987546 | 3 |
| #17987545 | 3 |
| #17987544 | 3 |
| C19⋊H(5,𝔽3) | 3 |
| C3×#13095333 | 3 |
| C3×#13095331 | 3 |
| C19⋊C3×#737 | 3 |
| C19×3−1+4 | 3 |
| #10624943 | 19 |