Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
406 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20293351 | C2 | semidirect |
| 2. #20293298 | C2 | semidirect |
| 3. #20293013 | C2 | semidirect |
| 4. #20293001 | C2 | semidirect |
| 5. #20292845 | C2 | semidirect |
| 6. #20292825 | C2 | semidirect |
| 7. #20292823 | C2 | semidirect |
| 8. #20292754 | C2 | semidirect |
| 9. #20292730 | C2 | semidirect |
| 10. C4×#13133803 | C2 | semidirect |
| 11. #461×C107 | C2 | semidirect |
| 106. C107⋊C8 | #41 | semidirect |
| 133. C107 | #3397 | semidirect |
| 139. #461 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293351 | 2 |
| #20293298 | 2 |
| #20293013 | 2 |
| #20293001 | 2 |
| #20292845 | 2 |
| #20292825 | 2 |
| #20292823 | 2 |
| #20292754 | 2 |
| #20292730 | 2 |
| C4×#13133803 | 2 |
| #461×C107 | 2 |
| #3397 | 107 |