Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20292655 | C2 | semidirect |
| 4. #20292398 | C2 | semidirect |
| 66. C107 | #1868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292655 | 2 |
| #20292601 | 2 |
| #20292594 | 2 |
| #20292398 | 2 |
| #568×C107 | 2 |
| #1868 | 107 |