Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
504 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 86 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⋊#349 | C2 | semidirect |
| 2. #20289650 | C2 | semidirect |
| 3. #20289649 | C2 | semidirect |
| 7. #16811519 | C22 | semidirect |
| 189. C53 | #11438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#349 | 2 |
| #20289650 | 2 |
| #20289649 | 2 |
| #20283157 | 2 |
| #11438 | 53 |