Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 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. #20293355 | C2 | semidirect |
| 2. #20292981 | C2 | semidirect |
| 4. #20292927 | C2 | semidirect |
| 5. #20292912 | C2 | semidirect |
| 6. #20292846 | C2 | semidirect |
| 8. Q8×C107⋊C8 | C2 | semidirect |
| 9. C4×#13133808 | C2 | semidirect |
| 10. C4×#13133806 | C2 | semidirect |
| 118. C107 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293355 | 2 |
| #20292981 | 2 |
| #20292973 | 2 |
| #20292927 | 2 |
| #20292912 | 2 |
| #20292846 | 2 |
| #20292824 | 2 |
| Q8×C107⋊C8 | 2 |
| C4×#13133808 | 2 |
| C4×#13133806 | 2 |
| #559×C107 | 2 |
| #3365 | 107 |