Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×Dic856 | C2 | semidirect |
| 3. #20292453 | C2 | semidirect |
| 4. #20292432 | C2 | semidirect |
| 42. C22×C107 | Q32 | semidirect |
| 54. C107 | #2216 | semidirect |
| 96. C22 | Dic856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic856 | 2 |
| #20292868 | 2 |
| #20292453 | 2 |
| #20292432 | 2 |
| C22×C16×C107 | 2 |
| #2216 | 107 |