Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 175. C53 | #9861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285225 | 2 |
| #20274886 | 2 |
| #20273171 | 2 |
| #20273170 | 2 |
| #20273169 | 2 |
| C2×#16810345 | 2 |
| C53×#1493 | 2 |
| #9861 | 53 |