Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
716 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14529102 | C2 | semidirect |
| 2. C2×#11762543 | C2 | semidirect |
| 3. #14527040 | C2 | semidirect |
| 4. #14526627 | C2 | semidirect |
| 51. #10587502 | D4 | semidirect |
| 280. C17 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14529102 | 2 |
| C2×#11762543 | 2 |
| #14527040 | 2 |
| #14526627 | 2 |
| C17×#2656 | 2 |
| #10403 | 17 |