Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 8. #16810587 | C4 | semidirect |
| 13. C53×#407 | C4 | semidirect |
| 150. #407 | Dic53 | semidirect |
| 152. C53 | #7319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274643 | 2 |
| #20274633 | 2 |
| C53×#1785 | 2 |
| #7319 | 53 |