Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
204 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 58 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. #17987439 | C3 | semidirect |
| 2. #17987438 | C3 | semidirect |
| 4. C19⋊#6862 | C3 | semidirect |
| 5. #17987324 | C3 | semidirect |
| 8. #17987317 | C3 | semidirect |
| 9. #17987317 | C3 | semidirect |
| 10. #17987315 | C3 | semidirect |
| 11. #17987315 | C3 | semidirect |
| 13. C19×#6887 | C3 | semidirect |
| 64. #6887 | C19⋊C3 | semidirect |
| 149. C19 | #10624606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987439 | 3 |
| #17987438 | 3 |
| C9×C32⋊(C19⋊C3) | 3 |
| C19⋊#6862 | 3 |
| #17987324 | 3 |
| #17987320 | 3 |
| #17987317 | 3 |
| #17987315 | 3 |
| #17987313 | 3 |
| C19×#6887 | 3 |
| #10624606 | 19 |