Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
716 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14529099 | C2 | semidirect |
| 3. C2×#11762544 | C2 | semidirect |
| 4. #14527040 | C2 | semidirect |
| 5. C17×#1280 | C2 | semidirect |
| 52. #10587502 | D4 | semidirect |
| 182. #1280 | D17 | semidirect |
| 280. C17 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14534886 | 2 |
| #14529099 | 2 |
| C2×#11762544 | 2 |
| #14527040 | 2 |
| C17×#1280 | 2 |
| #10403 | 17 |