Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 11. #16810908 | C4 | semidirect |
| 12. #16810833 | C4 | semidirect |
| 201. C53 | #9324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284845 | 2 |
| #20277080 | 2 |
| #20275659 | 2 |
| #20273228 | 2 |
| #20272609 | 2 |
| #20272570 | 2 |
| C53×#1491 | 2 |
| #9324 | 53 |