Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20275705 | C2 | semidirect |
| 5. #20272625 | C2 | semidirect |
| 6. #20272586 | C2 | semidirect |
| 7. C53×#1558 | C2 | semidirect |
| 180. #1558 | D53 | semidirect |
| 214. C53 | #9337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285742 | 2 |
| #20283887 | 2 |
| #20275705 | 2 |
| #20273323 | 2 |
| #20272625 | 2 |
| #20272586 | 2 |
| C53×#1558 | 2 |
| #9337 | 53 |