Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
364 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #20292756 | C2 | semidirect |
| 3. #20292751 | C2 | semidirect |
| 33. C2×C107⋊C8 | Q8 | semidirect |
| 84. C107 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293180 | 2 |
| #20292756 | 2 |
| #20292751 | 2 |
| #20292653 | 2 |
| #20292650 | 2 |
| #20292585 | 2 |
| #20292583 | 2 |
| C2×C8×Dic107 | 2 |
| #424×C107 | 2 |
| #2960 | 107 |