Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
406 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20293299 | C2 | semidirect |
| 2. #20293017 | C2 | semidirect |
| 3. #20293001 | C2 | semidirect |
| 4. #20292839 | C2 | semidirect |
| 5. #20292829 | C2 | semidirect |
| 6. #20292827 | C2 | semidirect |
| 7. #20292822 | C2 | semidirect |
| 8. #20292758 | C2 | semidirect |
| 9. #20292725 | C2 | semidirect |
| 10. C4×#13133803 | C2 | semidirect |
| 11. #556×C107 | C2 | semidirect |
| 106. C107⋊C8 | #41 | semidirect |
| 133. C107 | #3397 | semidirect |
| 134. #556 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293299 | 2 |
| #20293017 | 2 |
| #20293001 | 2 |
| #20292839 | 2 |
| #20292829 | 2 |
| #20292827 | 2 |
| #20292822 | 2 |
| #20292758 | 2 |
| #20292725 | 2 |
| C4×#13133803 | 2 |
| #556×C107 | 2 |
| #3397 | 107 |