Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
318 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14530981 | C2 | semidirect |
| 3. #14530225 | C2 | semidirect |
| 4. #14526803 | C2 | semidirect |
| 5. #14526799 | C2 | semidirect |
| 6. #14526709 | C2 | semidirect |
| 7. C17×#2233 | C2 | semidirect |
| 135. #2233 | D17 | semidirect |
| 216. C17 | #12285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539680 | 2 |
| #14530981 | 2 |
| #14530225 | 2 |
| #14526803 | 2 |
| #14526799 | 2 |
| #14526709 | 2 |
| C17×#2233 | 2 |
| #12285 | 17 |