Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
818 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 167. C53 | #28170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810833 | 2 |
| #20277434 | 2 |
| #20276134 | 2 |
| #20275815 | 2 |
| #20275059 | 2 |
| #20274835 | 2 |
| #20274730 | 2 |
| C53×#2327 | 2 |
| #28170 | 53 |