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.
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×#13095332 | C3 | semidirect |
| 7. C19⋊C3×#737 | C3 | semidirect |
| 8. C3×C19×#737 | C3 | semidirect |
| 9. #13095333 | C32 | semidirect |
| 10. #13095332 | C32 | semidirect |
| 11. #13095332 | C32 | semidirect |
| 12. #13095332 | C32 | semidirect |
| 13. #13095332 | C32 | semidirect |
| 14. #13095332 | C32 | semidirect |
| 15. #13095331 | C32 | semidirect |
| 16. C3×#10587025 | C32 | semidirect |
| 17. C3×#10587022 | C32 | semidirect |
| 18. C3×#10587023 | C32 | semidirect |
| 19. 3−1+2×C19⋊C3 | C32 | semidirect |
| 22. C3×C9×C19⋊C3 | C32 | semidirect |
| 23. C19×#737 | C32 | semidirect |
| 24. C19×#737 | C32 | semidirect |
| 25. C19×#737 | C32 | semidirect |
| 26. C3×C19×3−1+2 | C32 | semidirect |
| 28. C32×C9×C19 | C32 | semidirect |
| 57. C3×#737 | C19⋊C3 | semidirect |
| 75. #737 | C3×C19⋊C3 | semidirect |
| 76. #737 | C3×C19⋊C3 | semidirect |
| 77. #737 | C3×C19⋊C3 | semidirect |
| 82. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 87. C32×C9 | C3×C19⋊C3 | semidirect |
| 112. 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×#13095332 | 3 |
| C19⋊C3×#737 | 3 |
| C3×C19×#737 | 3 |
| #10624943 | 19 |