Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20277079 | C2 | semidirect |
| 5. #20273161 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 7. C53×#1285 | C2 | semidirect |
| 12. #16810919 | C4 | semidirect |
| 13. #16810824 | C4 | semidirect |
| 153. Dic106 | #104 | semidirect |
| 184. #1285 | D53 | semidirect |
| 212. C53 | #9326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284838 | 2 |
| #20277079 | 2 |
| #20275633 | 2 |
| #20273224 | 2 |
| #20273161 | 2 |
| #20272607 | 2 |
| C53×#1285 | 2 |
| #9326 | 53 |