Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 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. Q8×Dic214 | C2 | semidirect |
| 3. #20292977 | C2 | semidirect |
| 5. #20292912 | C2 | semidirect |
| 7. #20292834 | C2 | semidirect |
| 8. #20292758 | C2 | semidirect |
| 9. #20292732 | C2 | semidirect |
| 117. C107 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic214 | 2 |
| #20292986 | 2 |
| #20292977 | 2 |
| #20292917 | 2 |
| #20292912 | 2 |
| #20292846 | 2 |
| #20292834 | 2 |
| #20292758 | 2 |
| #20292732 | 2 |
| C4×#13133806 | 2 |
| #556×C107 | 2 |
| #3369 | 107 |