Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
256 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 2. #20272659 | C2 | semidirect |
| 3. C53×#1324 | C2 | semidirect |
| 16. #13133214 | C8 | semidirect |
| 97. #1324 | D53 | semidirect |
| 111. C53 | #7352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275538 | 2 |
| #20272659 | 2 |
| C53×#1324 | 2 |
| #7352 | 53 |