Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
418 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 418 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. #20293362 | C2 | semidirect |
| 2. #20293014 | C2 | semidirect |
| 3. #20293003 | C2 | semidirect |
| 4. #20292842 | C2 | semidirect |
| 5. #20292824 | C2 | semidirect |
| 6. #20292822 | C2 | semidirect |
| 7. #20292819 | C2 | semidirect |
| 8. #20292758 | C2 | semidirect |
| 9. #20292737 | C2 | semidirect |
| 10. C4×#13133806 | C2 | semidirect |
| 11. #550×C107 | C2 | semidirect |
| 108. C107⋊C8 | #41 | semidirect |
| 135. C107 | #3399 | semidirect |
| 137. #550 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293362 | 2 |
| #20293014 | 2 |
| #20293003 | 2 |
| #20292842 | 2 |
| #20292824 | 2 |
| #20292822 | 2 |
| #20292819 | 2 |
| #20292758 | 2 |
| #20292737 | 2 |
| C4×#13133806 | 2 |
| #550×C107 | 2 |
| #3399 | 107 |