Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
198 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 46 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⋊C3×#733 | C3 | semidirect |
| 3. #17987403 | C3 | semidirect |
| 4. #17987372 | C3 | semidirect |
| 5. #17987371 | C3 | semidirect |
| 6. #17987370 | C3 | semidirect |
| 7. #17987369 | C3 | semidirect |
| 8. #17987368 | C3 | semidirect |
| 9. C19×#6878 | C3 | semidirect |
| 13. #13095322 | C32 | semidirect |
| 14. #13095322 | C32 | semidirect |
| 21. C9×#4294 | C32 | semidirect |
| 22. C19×#733 | C32 | semidirect |
| 24. C92×C19 | C32 | semidirect |
| 52. #6878 | C19⋊C3 | semidirect |
| 74. #733 | C3×C19⋊C3 | semidirect |
| 82. C92 | C3×C19⋊C3 | semidirect |
| 108. C19 | #10624838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C19⋊C3×#733 | 3 |
| C19⋊C3×#732 | 3 |
| #17987403 | 3 |
| #17987372 | 3 |
| #17987371 | 3 |
| #17987370 | 3 |
| #17987369 | 3 |
| #17987368 | 3 |
| C19×#6878 | 3 |
| #10624838 | 19 |