Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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. #14530565 | C2 | semidirect |
| 3. #14526983 | C2 | semidirect |
| 4. #14526963 | C2 | semidirect |
| 5. #14526961 | C2 | semidirect |
| 6. #14526921 | C2 | semidirect |
| 7. C17×#1424 | C2 | semidirect |
| 72. #1424 | D17 | semidirect |
| 123. C17 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530871 | 2 |
| #14530565 | 2 |
| #14526983 | 2 |
| #14526963 | 2 |
| #14526961 | 2 |
| #14526921 | 2 |
| C17×#1424 | 2 |
| #13713 | 17 |