Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20293182 | C2 | semidirect |
| 3. #20292967 | C2 | semidirect |
| 4. #20292923 | C2 | semidirect |
| 5. #20292917 | C2 | semidirect |
| 6. #20292834 | C2 | semidirect |
| 8. #20292731 | C2 | semidirect |
| 9. #20292728 | C2 | semidirect |
| 10. #20292683 | C2 | semidirect |
| 11. #461×C107 | C2 | semidirect |
| 137. C107 | #3116 | semidirect |
| 144. #461 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293182 | 2 |
| C4×#13133817 | 2 |
| #20292967 | 2 |
| #20292923 | 2 |
| #20292917 | 2 |
| #20292834 | 2 |
| #20292786 | 2 |
| #20292731 | 2 |
| #20292728 | 2 |
| #20292683 | 2 |
| #461×C107 | 2 |
| #3116 | 107 |