Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20293156 | C2 | semidirect |
| 2. #20293029 | C2 | semidirect |
| 3. #20292981 | C2 | semidirect |
| 4. #20292865 | C2 | semidirect |
| 6. #20292853 | C2 | semidirect |
| 7. Q16×Dic107 | C2 | semidirect |
| 8. SD16×Dic107 | C2 | semidirect |
| 9. D8×Dic107 | C2 | semidirect |
| 10. C4×C8×D107 | C2 | semidirect |
| 11. #495×C107 | C2 | semidirect |
| 119. C107 | #3168 | semidirect |
| 122. #495 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293156 | 2 |
| #20293029 | 2 |
| #20292981 | 2 |
| #20292865 | 2 |
| #20292860 | 2 |
| #20292853 | 2 |
| Q16×Dic107 | 2 |
| SD16×Dic107 | 2 |
| D8×Dic107 | 2 |
| C4×C8×D107 | 2 |
| #495×C107 | 2 |
| #3168 | 107 |