Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
634 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 16. #16810388 | C4 | semidirect |
| 17. #16810387 | C4 | semidirect |
| 18. C53×#341 | C4 | semidirect |
| 178. #341 | #6157 | semidirect |
| 181. C53 | #11270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133286 | 2 |
| C2×#16811502 | 2 |
| #20290403 | 2 |
| #20290380 | 2 |
| #341×D53 | 2 |
| #11270 | 53 |