Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283821 | C2 | semidirect |
| 2. #20273425 | C2 | semidirect |
| 5. #20272627 | C2 | semidirect |
| 6. #20272578 | C2 | semidirect |
| 180. C53 | #9334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283821 | 2 |
| #20273425 | 2 |
| #20273339 | 2 |
| #20273067 | 2 |
| #20272627 | 2 |
| #20272578 | 2 |
| C53×#3215 | 2 |
| #9334 | 53 |