Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276400 | C2 | semidirect |
| 2. #20273450 | C2 | semidirect |
| 3. #20272869 | C2 | semidirect |
| 7. #16810422 | C22 | semidirect |
| 9. #16810372 | C22 | semidirect |
| 196. C53 | #13574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276400 | 2 |
| #20273450 | 2 |
| #20272869 | 2 |
| C53×#3018 | 2 |
| #13574 | 53 |