Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 25. C2×Dic214 | C8 | semidirect |
| 35. C2×C107⋊C8 | Q8 | semidirect |
| 51. C2×C8×C107 | Q8 | semidirect |
| 109. C107 | #1984 | semidirect |
| 153. C2×C8 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic214 | 2 |
| C2×Dic107⋊C8 | 2 |
| C2×C8×Dic107 | 2 |
| #20292382 | 2 |
| #20292381 | 2 |
| #336×C107 | 2 |
| #1984 | 107 |