Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
806 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 806 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. #14539921 | C2 | semidirect |
| 2. #14539721 | C2 | semidirect |
| 3. #14539530 | C2 | semidirect |
| 5. #14528453 | C2 | semidirect |
| 6. #14528421 | C2 | semidirect |
| 7. #14528413 | C2 | semidirect |
| 8. #14528409 | C2 | semidirect |
| 9. #14528390 | C2 | semidirect |
| 10. #14527078 | C2 | semidirect |
| 11. C17×#1705 | C2 | semidirect |
| 16. #11763212 | C22 | semidirect |
| 18. #11763189 | C22 | semidirect |
| 23. #11763161 | C22 | semidirect |
| 24. #11763157 | C22 | semidirect |
| 26. #11763156 | C22 | semidirect |
| 36. #11762531 | C22 | semidirect |
| 37. #11762530 | C22 | semidirect |
| 38. C17×#498 | C22 | semidirect |
| 39. C17×#498 | C22 | semidirect |
| 42. C82×C17 | C22 | semidirect |
| 174. #1705 | D17 | semidirect |
| 198. #498 | C2×D17 | semidirect |
| 199. #498 | C2×D17 | semidirect |
| 223. C82 | C2×D17 | semidirect |
| 275. C17 | #19713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539921 | 2 |
| #14539721 | 2 |
| #14539530 | 2 |
| #14539231 | 2 |
| #14528453 | 2 |
| #14528421 | 2 |
| #14528413 | 2 |
| #14528409 | 2 |
| #14528390 | 2 |
| #14527078 | 2 |
| C17×#1705 | 2 |
| #19713 | 17 |