Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
258 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 258 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 |
|---|---|---|
| 1. #20289760 | C2 | semidirect |
| 2. #20289537 | C2 | semidirect |
| 20. C2×Dic212 | C8 | semidirect |
| 22. C2×D424 | C8 | semidirect |
| 123. C53 | #7114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289760 | 2 |
| #20289537 | 2 |
| #20275601 | 2 |
| #7114 | 53 |