Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
184 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 52 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. #17987438 | C3 | semidirect |
| 3. C19⋊#6862 | C3 | semidirect |
| 4. #17987324 | C3 | semidirect |
| 6. #17987317 | C3 | semidirect |
| 7. #17987315 | C3 | semidirect |
| 9. C19×#6895 | C3 | semidirect |
| 42. #6895 | C19⋊C3 | semidirect |
| 103. C19 | #10624676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987438 | 3 |
| #17987426 | 3 |
| C19⋊#6862 | 3 |
| #17987324 | 3 |
| #17987320 | 3 |
| #17987317 | 3 |
| #17987315 | 3 |
| #17987313 | 3 |
| C19×#6895 | 3 |
| #10624676 | 19 |