Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #14526606 | C2 | semidirect |
| 196. C17 | #7705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537136 | 2 |
| #14528546 | 2 |
| #14526606 | 2 |
| C17×#1817 | 2 |
| #7705 | 17 |