Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
788 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 788 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. #14539742 | C2 | semidirect |
| 2. #14539704 | C2 | semidirect |
| 3. #14539522 | C2 | semidirect |
| 4. #14539159 | C2 | semidirect |
| 5. #14528450 | C2 | semidirect |
| 6. #14528444 | C2 | semidirect |
| 7. #14528423 | C2 | semidirect |
| 8. #14528390 | C2 | semidirect |
| 9. C17×#1453 | C2 | semidirect |
| 13. #11763207 | C22 | semidirect |
| 14. #11763189 | C22 | semidirect |
| 17. #11763186 | C22 | semidirect |
| 18. #11763182 | C22 | semidirect |
| 20. #11763160 | C22 | semidirect |
| 25. #11763156 | C22 | semidirect |
| 26. #11763156 | C22 | semidirect |
| 36. C17×#322 | C22 | semidirect |
| 37. C17×#322 | C22 | semidirect |
| 38. C82×C17 | C22 | semidirect |
| 157. #1453 | D17 | semidirect |
| 200. #322 | C2×D17 | semidirect |
| 201. #322 | C2×D17 | semidirect |
| 202. C82 | C2×D17 | semidirect |
| 248. C17 | #19729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539742 | 2 |
| #14539704 | 2 |
| #14539522 | 2 |
| #14539159 | 2 |
| #14528450 | 2 |
| #14528444 | 2 |
| #14528423 | 2 |
| #14528390 | 2 |
| C17×#1453 | 2 |
| #19729 | 17 |