Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
446 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #14526690 | C2 | semidirect |
| 5. #14526670 | C2 | semidirect |
| 6. #14526636 | C2 | semidirect |
| 7. C17×#2665 | C2 | semidirect |
| 30. C22×D68 | Q8 | semidirect |
| 46. C2×C4⋊Dic17 | Q8 | semidirect |
| 172. #2665 | D17 | semidirect |
| 276. C17 | #10382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14529619 | 2 |
| #14527312 | 2 |
| #14527299 | 2 |
| #14526690 | 2 |
| #14526670 | 2 |
| #14526636 | 2 |
| C17×#2665 | 2 |
| #10382 | 17 |