Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
620 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 256 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. #17987452 | C3 | semidirect |
| 2. #17987447 | C3 | semidirect |
| 3. #17987441 | C3 | semidirect |
| 4. #17987440 | C3 | semidirect |
| 7. #17987415 | C3 | semidirect |
| 15. #13095307 | C32 | semidirect |
| 16. #13095306 | C32 | semidirect |
| 17. #13095305 | C32 | semidirect |
| 18. #13095305 | C32 | semidirect |
| 19. #13095305 | C32 | semidirect |
| 26. C9×#4294 | C32 | semidirect |
| 127. C19 | #10624889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #17987452 | 3 |
| #17987447 | 3 |
| #17987441 | 3 |
| #17987440 | 3 |
| #17987421 | 3 |
| #17987415 | 3 |
| C3×C32⋊#4294 | 3 |
| C19×#6891 | 3 |
| #10624889 | 19 |