Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
388 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 75 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. #16810392 | C4 | semidirect |
| 10. C22×M16×C53 | C4 | semidirect |
| 13. C2×C22⋊C8×C53 | C4 | semidirect |
| 148. C22×M16 | Dic53 | semidirect |
| 153. C2×C22⋊C8 | Dic53 | semidirect |
| 159. C53 | #7282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133134 | 2 |
| C4×#13133132 | 2 |
| C53×#1870 | 2 |
| #7282 | 53 |