Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
258 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 39 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. #20272836 | C2 | semidirect |
| 2. #20272653 | C2 | semidirect |
| 7. C22×D8×C53 | C4 | semidirect |
| 10. C53×#341 | C4 | semidirect |
| 105. C22×D8 | Dic53 | semidirect |
| 110. #341 | Dic53 | semidirect |
| 111. C53 | #7398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272836 | 2 |
| #20272653 | 2 |
| C53×#2018 | 2 |
| #7398 | 53 |