Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20293255 | C2 | semidirect |
| 2. #20292991 | C2 | semidirect |
| 3. #20292986 | C2 | semidirect |
| 4. #20292981 | C2 | semidirect |
| 5. #20292973 | C2 | semidirect |
| 6. #20292632 | C2 | semidirect |
| 7. #20292628 | C2 | semidirect |
| 8. #20292623 | C2 | semidirect |
| 9. C2×#16812030 | C2 | semidirect |
| 10. #20292583 | C2 | semidirect |
| 14. #16812109 | C22 | semidirect |
| 16. #16812101 | C22 | semidirect |
| 21. #16812033 | C22 | semidirect |
| 22. #16812033 | C22 | semidirect |
| 23. #16812033 | C22 | semidirect |
| 28. #16812030 | C22 | semidirect |
| 29. #16812030 | C22 | semidirect |
| 30. #16812030 | C22 | semidirect |
| 31. #16812020 | C22 | semidirect |
| 32. C4×C107⋊C8 | C22 | semidirect |
| 136. C107 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20292991 | 2 |
| #20292986 | 2 |
| #20292981 | 2 |
| #20292973 | 2 |
| #20292632 | 2 |
| #20292628 | 2 |
| #20292623 | 2 |
| C2×#16812030 | 2 |
| #20292583 | 2 |
| #535×C107 | 2 |
| #3136 | 107 |