Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20293347 | C2 | semidirect |
| 2. #20292977 | C2 | semidirect |
| 3. #20292965 | C2 | semidirect |
| 4. #20292907 | C2 | semidirect |
| 5. #20292866 | C2 | semidirect |
| 6. #20292834 | C2 | semidirect |
| 7. #20292789 | C2 | semidirect |
| 8. C4×#13133806 | C2 | semidirect |
| 9. D4×C107⋊C8 | C2 | semidirect |
| 10. #20292623 | C2 | semidirect |
| 126. C107 | #3302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293347 | 2 |
| #20292977 | 2 |
| #20292965 | 2 |
| #20292907 | 2 |
| #20292866 | 2 |
| #20292834 | 2 |
| #20292789 | 2 |
| C4×#13133806 | 2 |
| D4×C107⋊C8 | 2 |
| #20292623 | 2 |
| #547×C107 | 2 |
| #3302 | 107 |