Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
842 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 7. C2×#13133127 | C4 | semidirect |
| 8. C2×C8×Dic53 | C4 | semidirect |
| 9. #16810380 | C4 | semidirect |
| 11. C53×#338 | C4 | semidirect |
| 95. #338 | Dic53 | semidirect |
| 97. C53 | #10699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810581 | 2 |
| C2×#16810380 | 2 |
| C2×C53×#338 | 2 |
| #10699 | 53 |