Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1030 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 2. C2×#16811483 | C2 | semidirect |
| 131. C22×C53 | #333 | semidirect |
| 165. C53 | #8342 | semidirect |
| 280. C22 | #16811483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290571 | 2 |
| C2×#16811483 | 2 |
| C22×#13133215 | 2 |
| #8342 | 53 |