Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 80 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. D53⋊(C22⋊C16) | C2 | semidirect |
| 2. #20290591 | C2 | semidirect |
| 3. #20289704 | C2 | semidirect |
| 4. #20289702 | C2 | semidirect |
| 12. C2×#13133239 | C4 | semidirect |
| 15. #16810865 | C4 | semidirect |
| 17. #16810860 | C4 | semidirect |
| 22. C53×#427 | C4 | semidirect |
| 187. #427 | #6157 | semidirect |
| 194. C53 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊(C22⋊C16) | 2 |
| #20290591 | 2 |
| #20289704 | 2 |
| #20289702 | 2 |
| #20284297 | 2 |
| #11885 | 53 |