Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
420 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 80 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. #14544669 | C2 | semidirect |
| 3. #14543876 | C2 | semidirect |
| 189. C17 | #12809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545077 | 2 |
| #14544669 | 2 |
| #14543876 | 2 |
| #14537495 | 2 |
| #12809 | 17 |