Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
174 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 7. #13095339 | C9 | semidirect |
| 10. #13095338 | C9 | semidirect |
| 16. C9×#4296 | C9 | semidirect |
| 18. #13095307 | C9 | semidirect |
| 19. #13095306 | C9 | semidirect |
| 23. C19×C9⋊C9 | C9 | semidirect |
| 78. C9⋊C9 | #4296 | semidirect |
| 111. C19 | #10624470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987589 | 3 |
| #17987404 | 3 |
| #10624470 | 19 |