Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
1062 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 268 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. C19⋊H(5,𝔽3) | C3 | semidirect |
| 2. C3×#13095333 | C3 | semidirect |
| 3. #17987515 | C3 | semidirect |
| 4. #17987514 | C3 | semidirect |
| 5. #17987513 | C3 | semidirect |
| 6. #17987512 | C3 | semidirect |
| 7. C3×#13095319 | C3 | semidirect |
| 8. C19⋊C3×#732 | C3 | semidirect |
| 9. C19×#6911 | C3 | semidirect |
| 11. C3×#10587025 | C32 | semidirect |
| 12. C3×#10587022 | C32 | semidirect |
| 13. C3×#10587023 | C32 | semidirect |
| 16. C3×C32⋊(C19⋊C3) | C32 | semidirect |
| 18. H(3,𝔽3)×C19⋊C3 | C32 | semidirect |
| 19. C32×#4294 | C32 | semidirect |
| 20. C3×C9×C19⋊C3 | C32 | semidirect |
| 21. #13095320 | C32 | semidirect |
| 22. #13095319 | C32 | semidirect |
| 23. #13095319 | C32 | semidirect |
| 24. #13095319 | C32 | semidirect |
| 25. #13095319 | C32 | semidirect |
| 26. C3×C19×3−1+2 | C32 | semidirect |
| 27. C3×C19×H(3,𝔽3) | C32 | semidirect |
| 28. C19×#732 | C32 | semidirect |
| 59. #6911 | C19⋊C3 | semidirect |
| 81. C3×3−1+2 | C3×C19⋊C3 | semidirect |
| 87. C3×H(3,𝔽3) | C3×C19⋊C3 | semidirect |
| 95. #732 | C3×C19⋊C3 | semidirect |
| 125. C19 | #10624932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19⋊H(5,𝔽3) | 3 |
| C3×#13095333 | 3 |
| #17987515 | 3 |
| #17987514 | 3 |
| #17987513 | 3 |
| #17987512 | 3 |
| C3×#13095319 | 3 |
| C19⋊C3×#732 | 3 |
| C19×#6911 | 3 |
| #10624932 | 19 |