Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
404 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 26. #13133136 | Q8 | semidirect |
| 157. C53 | #13301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274711 | 2 |
| C4×#13133136 | 2 |
| #20272842 | 2 |
| C53×#2568 | 2 |
| #13301 | 53 |