Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
374 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×#13095306 | C3 | semidirect |
| 2. C3×#13095305 | C3 | semidirect |
| 7. #17987308 | C3 | semidirect |
| 8. #17987308 | C3 | semidirect |
| 9. #17987308 | C3 | semidirect |
| 10. #17987308 | C3 | semidirect |
| 11. #17987308 | C3 | semidirect |
| 12. #17987308 | C3 | semidirect |
| 13. C3×C19×C9⋊C9 | C3 | semidirect |
| 99. C3×C9⋊C9 | C19⋊C3 | semidirect |
| 244. C19 | #10624566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#13095306 | 3 |
| C3×#13095305 | 3 |
| C3×#13095303 | 3 |
| #17987308 | 3 |
| C3×C19×C9⋊C9 | 3 |
| #10624566 | 19 |