Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
798 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 159 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. #14539913 | C2 | semidirect |
| 2. #14539720 | C2 | semidirect |
| 3. #14539523 | C2 | semidirect |
| 4. #14539242 | C2 | semidirect |
| 5. #14528450 | C2 | semidirect |
| 6. #14528441 | C2 | semidirect |
| 7. #14528413 | C2 | semidirect |
| 8. #14528391 | C2 | semidirect |
| 9. #14528372 | C2 | semidirect |
| 10. #14527082 | C2 | semidirect |
| 11. C17×#1716 | C2 | semidirect |
| 171. #1716 | D17 | semidirect |
| 273. C17 | #19721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539913 | 2 |
| #14539720 | 2 |
| #14539523 | 2 |
| #14539242 | 2 |
| #14528450 | 2 |
| #14528441 | 2 |
| #14528413 | 2 |
| #14528391 | 2 |
| #14528372 | 2 |
| #14527082 | 2 |
| C17×#1716 | 2 |
| #19721 | 17 |