Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
360 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 69 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. #14531009 | C2 | semidirect |
| 3. #14528180 | C2 | semidirect |
| 4. #14526831 | C2 | semidirect |
| 5. #14526748 | C2 | semidirect |
| 6. #14526738 | C2 | semidirect |
| 7. C17×#2227 | C2 | semidirect |
| 121. #2227 | D17 | semidirect |
| 193. C17 | #12373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14540543 | 2 |
| #14531009 | 2 |
| #14528180 | 2 |
| #14526831 | 2 |
| #14526748 | 2 |
| #14526738 | 2 |
| C17×#2227 | 2 |
| #12373 | 17 |