Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
884 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 230 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 |
|---|---|---|
| 151. C53 | #17430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291618 | 2 |
| #20289988 | 2 |
| #20289977 | 2 |
| #20289957 | 2 |
| C2×#16811349 | 2 |
| #17430 | 53 |