Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 172. C53 | #11865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285296 | 2 |
| #20276515 | 2 |
| #20274851 | 2 |
| #20272734 | 2 |
| #20272733 | 2 |
| #20272732 | 2 |
| C53×#1350 | 2 |
| #11865 | 53 |