Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #20293338 | C2 | semidirect |
| 3. #20292970 | C2 | semidirect |
| 4. #20292942 | C2 | semidirect |
| 5. #20292919 | C2 | semidirect |
| 6. #20292914 | C2 | semidirect |
| 7. #20292874 | C2 | semidirect |
| 8. C4×#13133807 | C2 | semidirect |
| 9. #20292706 | C2 | semidirect |
| 10. #20292668 | C2 | semidirect |
| 11. #500×C107 | C2 | semidirect |
| 122. C107 | #3357 | semidirect |
| 125. #500 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293343 | 2 |
| #20293338 | 2 |
| #20292970 | 2 |
| #20292942 | 2 |
| #20292919 | 2 |
| #20292914 | 2 |
| #20292874 | 2 |
| C4×#13133807 | 2 |
| #20292706 | 2 |
| #20292668 | 2 |
| #500×C107 | 2 |
| #3357 | 107 |