Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 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×D428 | C2 | semidirect |
| 2. #20292986 | C2 | semidirect |
| 3. #20292973 | C2 | semidirect |
| 4. #20292917 | C2 | semidirect |
| 5. #20292912 | C2 | semidirect |
| 6. #20292839 | C2 | semidirect |
| 8. #20292758 | C2 | semidirect |
| 9. #20292737 | C2 | semidirect |
| 10. C4×#13133805 | C2 | semidirect |
| 11. #559×C107 | C2 | semidirect |
| 125. C107 | #3373 | semidirect |
| 126. #559 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D428 | 2 |
| #20292986 | 2 |
| #20292973 | 2 |
| #20292917 | 2 |
| #20292912 | 2 |
| #20292839 | 2 |
| #20292819 | 2 |
| #20292758 | 2 |
| #20292737 | 2 |
| C4×#13133805 | 2 |
| #559×C107 | 2 |
| #3373 | 107 |