Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
322 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 19. C2×#11719940 | C8 | semidirect |
| 25. C22×#88324 | C8 | semidirect |
| 161. C53 | #7188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290381 | 2 |
| #20289947 | 2 |
| #20273026 | 2 |
| #7188 | 53 |