Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20272801 | C2 | semidirect |
| 122. C53 | #12851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810405 | 2 |
| #20272801 | 2 |
| C53×#2873 | 2 |
| #12851 | 53 |