Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 1. #20290942 | C2 | semidirect |
| 2. C2×C22⋊#11719910 | C2 | semidirect |
| 3. #20289637 | C2 | semidirect |
| 9. C22⋊#11719910 | C22 | semidirect |
| 10. C22⋊#11719910 | C22 | semidirect |
| 183. C53 | #11422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290942 | 2 |
| C2×C22⋊#11719910 | 2 |
| #20289637 | 2 |
| C2×#16810590 | 2 |
| #11422 | 53 |