Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
692 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20272558 | C2 | semidirect |
| 16. C22×D4×C53 | C8 | semidirect |
| 162. C53 | #7103 | semidirect |
| 168. C22×D4 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272558 | 2 |
| C53×#1438 | 2 |
| #7103 | 53 |