Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 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. #20293334 | C2 | semidirect |
| 2. #20293030 | C2 | semidirect |
| 3. #20292968 | C2 | semidirect |
| 4. #20292938 | C2 | semidirect |
| 5. #20292919 | C2 | semidirect |
| 6. #20292917 | C2 | semidirect |
| 7. #20292871 | C2 | semidirect |
| 8. C4×#13133806 | C2 | semidirect |
| 9. #20292705 | C2 | semidirect |
| 10. #20292670 | C2 | semidirect |
| 122. C107 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293334 | 2 |
| #20293030 | 2 |
| #20292968 | 2 |
| #20292938 | 2 |
| #20292919 | 2 |
| #20292917 | 2 |
| #20292871 | 2 |
| C4×#13133806 | 2 |
| #20292705 | 2 |
| #20292670 | 2 |
| #555×C107 | 2 |
| #3357 | 107 |