Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
874 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 874 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. #14539718 | C2 | semidirect |
| 2. #14539698 | C2 | semidirect |
| 3. #14539520 | C2 | semidirect |
| 4. #14539231 | C2 | semidirect |
| 5. #14528451 | C2 | semidirect |
| 6. #14528424 | C2 | semidirect |
| 7. #14528412 | C2 | semidirect |
| 8. #14528398 | C2 | semidirect |
| 9. #14528383 | C2 | semidirect |
| 10. #14527082 | C2 | semidirect |
| 11. C17×#1721 | C2 | semidirect |
| 16. #11763207 | C22 | semidirect |
| 21. #11763185 | C22 | semidirect |
| 23. #11763182 | C22 | semidirect |
| 24. #11763161 | C22 | semidirect |
| 27. #11763155 | C22 | semidirect |
| 36. #11762530 | C22 | semidirect |
| 37. C8×#3622 | C22 | semidirect |
| 39. C17×#493 | C22 | semidirect |
| 41. C17×#486 | C22 | semidirect |
| 42. C17×#322 | C22 | semidirect |
| 177. #1721 | D17 | semidirect |
| 213. #493 | C2×D17 | semidirect |
| 221. #486 | C2×D17 | semidirect |
| 231. #322 | C2×D17 | semidirect |
| 285. C17 | #19727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539718 | 2 |
| #14539698 | 2 |
| #14539520 | 2 |
| #14539231 | 2 |
| #14528451 | 2 |
| #14528424 | 2 |
| #14528412 | 2 |
| #14528398 | 2 |
| #14528383 | 2 |
| #14527082 | 2 |
| C17×#1721 | 2 |
| #19727 | 17 |