Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 290 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 |
|---|---|---|
| 2. #20272793 | C2 | semidirect |
| 3. C53×#1277 | C2 | semidirect |
| 15. C2×D424 | C8 | semidirect |
| 122. #1277 | D53 | semidirect |
| 138. C53 | #7112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275581 | 2 |
| #20272793 | 2 |
| C53×#1277 | 2 |
| #7112 | 53 |