Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
908 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 171 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. #14539522 | C2 | semidirect |
| 2. #14539503 | C2 | semidirect |
| 3. #14539234 | C2 | semidirect |
| 4. #14528452 | C2 | semidirect |
| 5. #14528420 | C2 | semidirect |
| 6. #14528405 | C2 | semidirect |
| 7. #14528375 | C2 | semidirect |
| 8. #14527087 | C2 | semidirect |
| 9. C17×#3138 | C2 | semidirect |
| 12. #11763212 | C22 | semidirect |
| 13. #11763207 | C22 | semidirect |
| 15. #11763186 | C22 | semidirect |
| 18. #11763183 | C22 | semidirect |
| 21. #11763159 | C22 | semidirect |
| 22. #11763157 | C22 | semidirect |
| 23. #11763156 | C22 | semidirect |
| 29. #11762531 | C22 | semidirect |
| 30. #11762530 | C22 | semidirect |
| 31. C8×#3622 | C22 | semidirect |
| 151. #3622 | AGL(1,ℤ/8) | semidirect |
| 155. #3138 | D17 | semidirect |
| 252. C17 | #19747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539522 | 2 |
| #14539503 | 2 |
| #14539234 | 2 |
| #14528452 | 2 |
| #14528420 | 2 |
| #14528405 | 2 |
| #14528375 | 2 |
| #14527087 | 2 |
| C17×#3138 | 2 |
| #19747 | 17 |