Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
712 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 323 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. #14527088 | C2 | semidirect |
| 3. #14527086 | C2 | semidirect |
| 4. #14527085 | C2 | semidirect |
| 5. #14527084 | C2 | semidirect |
| 6. #14527083 | C2 | semidirect |
| 7. C17×#1454 | C2 | semidirect |
| 18. #11762531 | C22 | semidirect |
| 19. #11762531 | C22 | semidirect |
| 20. #11762530 | C22 | semidirect |
| 21. C8×#3622 | C22 | semidirect |
| 23. C17×#322 | C22 | semidirect |
| 24. C82×C17 | C22 | semidirect |
| 92. #1454 | D17 | semidirect |
| 116. #322 | C2×D17 | semidirect |
| 118. C82 | C2×D17 | semidirect |
| 146. C17 | #17339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537412 | 2 |
| #14527088 | 2 |
| #14527086 | 2 |
| #14527085 | 2 |
| #14527084 | 2 |
| #14527083 | 2 |
| C17×#1454 | 2 |
| #17339 | 17 |