Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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. #20289856 | C2 | semidirect |
| 7. #16811180 | C4 | semidirect |
| 9. #16810992 | C4 | semidirect |
| 13. C2×#97×C53 | C4 | semidirect |
| 108. C2×#97 | #6157 | semidirect |
| 111. C53 | #13594 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290988 | 2 |
| #20289856 | 2 |
| #20285061 | 2 |
| #13594 | 53 |