Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
712 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 179 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. #14539914 | C2 | semidirect |
| 2. #14539742 | C2 | semidirect |
| 4. #14539165 | C2 | semidirect |
| 5. #14528444 | C2 | semidirect |
| 6. #14528423 | C2 | semidirect |
| 7. #14528417 | C2 | semidirect |
| 8. #14528385 | C2 | semidirect |
| 9. C17×#1453 | C2 | semidirect |
| 150. #1453 | D17 | semidirect |
| 237. C17 | #19724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539914 | 2 |
| #14539742 | 2 |
| #14539522 | 2 |
| #14539165 | 2 |
| #14528444 | 2 |
| #14528423 | 2 |
| #14528417 | 2 |
| #14528385 | 2 |
| C17×#1453 | 2 |
| #19724 | 17 |