Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 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 |
| 3. #20292977 | C2 | semidirect |
| 4. #20292934 | C2 | semidirect |
| 7. #20292834 | C2 | semidirect |
| 8. Q8×C107⋊C8 | C2 | semidirect |
| 9. C4×#13133808 | C2 | semidirect |
| 116. C107 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293355 | 2 |
| #20292981 | 2 |
| #20292977 | 2 |
| #20292934 | 2 |
| #20292907 | 2 |
| #20292846 | 2 |
| #20292834 | 2 |
| Q8×C107⋊C8 | 2 |
| C4×#13133808 | 2 |
| C4×#13133806 | 2 |
| #556×C107 | 2 |
| #3364 | 107 |