Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
564 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #14539722 | C2 | semidirect |
| 3. #14529608 | C2 | semidirect |
| 4. #14527348 | C2 | semidirect |
| 5. #14527344 | C2 | semidirect |
| 6. #14526629 | C2 | semidirect |
| 7. C17×#3135 | C2 | semidirect |
| 169. #3135 | D17 | semidirect |
| 272. C17 | #10219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539722 | 2 |
| #14539699 | 2 |
| #14529608 | 2 |
| #14527348 | 2 |
| #14527344 | 2 |
| #14526629 | 2 |
| C17×#3135 | 2 |
| #10219 | 17 |