Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 17. Dic428 | C8 | semidirect |
| 40. C107⋊C8 | Q16 | semidirect |
| 53. C107 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292751 | 2 |
| C4×Dic428 | 2 |
| #20292357 | 2 |
| C8×C107⋊C8 | 2 |
| #335×C107 | 2 |
| C8×Q16 | 107 |