Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20293255 | C2 | semidirect |
| 5. #20292395 | C2 | semidirect |
| 6. #20292387 | C2 | semidirect |
| 7. #339×C107 | C2 | semidirect |
| 32. C2×D428 | Q8 | semidirect |
| 113. C107 | #2027 | semidirect |
| 120. #339 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20292633 | 2 |
| #20292631 | 2 |
| #20292529 | 2 |
| #20292395 | 2 |
| #20292387 | 2 |
| #339×C107 | 2 |
| #2027 | 107 |