Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
326 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 8. C22⋊#11719910 | C4 | semidirect |
| 13. C22⋊#11719908 | C4 | semidirect |
| 15. C53×C22⋊C16 | C4 | semidirect |
| 151. C22⋊C16 | #6157 | semidirect |
| 154. C53 | #7186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| #20290380 | 2 |
| C22⋊C16×D53 | 2 |
| #7186 | 53 |