Finite Group DatabasebetaFinite Group DatabasebetaOrder 13851.
824 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 301 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 |
|---|---|---|
| 2. #17987443 | C3 | semidirect |
| 3. #17987434 | C3 | semidirect |
| 5. C9×#10587022 | C3 | semidirect |
| 6. #17987405 | C3 | semidirect |
| 7. C19×#6887 | C3 | semidirect |
| 14. #13095307 | C32 | semidirect |
| 15. #13095306 | C32 | semidirect |
| 16. #13095306 | C32 | semidirect |
| 17. #13095305 | C32 | semidirect |
| 20. C9×#4294 | C32 | semidirect |
| 22. C19×C9⋊C9 | C32 | semidirect |
| 24. C92×C19 | C32 | semidirect |
| 30. C3×C9×C19 | 3−1+2 | semidirect |
| 46. #6887 | C19⋊C3 | semidirect |
| 70. C9⋊C9 | C3×C19⋊C3 | semidirect |
| 75. C92 | C3×C19⋊C3 | semidirect |
| 90. C3×C9 | #10587022 | semidirect |
| 94. C19 | #10624872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C19⋊C3 | 3 |
| #17987443 | 3 |
| #17987434 | 3 |
| #17987420 | 3 |
| C9×#10587022 | 3 |
| #17987405 | 3 |
| C19×#6887 | 3 |
| #10624872 | 19 |