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 |
|---|---|---|
| 2. #20293030 | C2 | semidirect |
| 3. #20292965 | C2 | semidirect |
| 4. #20292940 | C2 | semidirect |
| 5. #20292922 | C2 | semidirect |
| 6. #20292914 | C2 | semidirect |
| 7. #20292875 | C2 | semidirect |
| 8. C4×#13133805 | C2 | semidirect |
| 9. #20292705 | C2 | semidirect |
| 10. #20292667 | C2 | semidirect |
| 11. #554×C107 | C2 | semidirect |
| 122. C107 | #3357 | semidirect |
| 124. #554 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293342 | 2 |
| #20293030 | 2 |
| #20292965 | 2 |
| #20292940 | 2 |
| #20292922 | 2 |
| #20292914 | 2 |
| #20292875 | 2 |
| C4×#13133805 | 2 |
| #20292705 | 2 |
| #20292667 | 2 |
| #554×C107 | 2 |
| #3357 | 107 |