Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
684 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 140 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. #20290648 | C2 | semidirect |
| 3. #20289593 | C2 | semidirect |
| 159. Dic53 | #331 | semidirect |
| 188. C53 | #8585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290648 | 2 |
| C2×#16811481 | 2 |
| #20289593 | 2 |
| #20277279 | 2 |
| #8585 | 53 |