Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×Dic428 | C2 | semidirect |
| 3. #20292885 | C2 | semidirect |
| 4. #20292868 | C2 | semidirect |
| 5. #20292665 | C2 | semidirect |
| 6. #20292637 | C2 | semidirect |
| 89. C107 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic428 | 2 |
| #20293198 | 2 |
| #20292885 | 2 |
| #20292868 | 2 |
| #20292665 | 2 |
| #20292637 | 2 |
| C2×#131×C107 | 2 |
| #3059 | 107 |