Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
720 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 720 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. #14539945 | C2 | semidirect |
| 3. #14539529 | C2 | semidirect |
| 5. #14528444 | C2 | semidirect |
| 6. #14528437 | C2 | semidirect |
| 7. #14528406 | C2 | semidirect |
| 8. #14528385 | C2 | semidirect |
| 9. C17×#1453 | C2 | semidirect |
| 13. #11763214 | C22 | semidirect |
| 14. #11763207 | C22 | semidirect |
| 15. #11763207 | C22 | semidirect |
| 16. #11763189 | C22 | semidirect |
| 20. #11763160 | C22 | semidirect |
| 21. #11763160 | C22 | semidirect |
| 22. #11763160 | C22 | semidirect |
| 36. C17×#322 | C22 | semidirect |
| 37. C17×#322 | C22 | semidirect |
| 38. C82×C17 | C22 | semidirect |
| 150. #1453 | D17 | semidirect |
| 191. #322 | C2×D17 | semidirect |
| 192. #322 | C2×D17 | semidirect |
| 193. C82 | C2×D17 | semidirect |
| 238. C17 | #19717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539945 | 2 |
| #14539727 | 2 |
| #14539529 | 2 |
| #14539159 | 2 |
| #14528444 | 2 |
| #14528437 | 2 |
| #14528406 | 2 |
| #14528385 | 2 |
| C17×#1453 | 2 |
| #19717 | 17 |