Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
574 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 107 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. #14531149 | C2 | semidirect |
| 5. #14526678 | C2 | semidirect |
| 6. #14526639 | C2 | semidirect |
| 7. C17×#1491 | C2 | semidirect |
| 11. #11763104 | C4 | semidirect |
| 12. #11763009 | C4 | semidirect |
| 122. Q8×C17 | #104 | semidirect |
| 162. #1491 | D17 | semidirect |
| 255. C17 | #9326 | semidirect |
| 306. Q8 | #10587496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538906 | 2 |
| #14531149 | 2 |
| #14529703 | 2 |
| #14527293 | 2 |
| #14526678 | 2 |
| #14526639 | 2 |
| C17×#1491 | 2 |
| #9326 | 17 |