Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
994 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 167 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. #14539523 | C2 | semidirect |
| 2. #14539521 | C2 | semidirect |
| 3. #14539235 | C2 | semidirect |
| 4. #14539231 | C2 | semidirect |
| 5. #14528452 | C2 | semidirect |
| 6. #14528450 | C2 | semidirect |
| 7. #14528411 | C2 | semidirect |
| 8. #14528398 | C2 | semidirect |
| 9. #14528372 | C2 | semidirect |
| 10. #14527088 | C2 | semidirect |
| 11. C17×#1715 | C2 | semidirect |
| 17. #11763205 | C22 | semidirect |
| 21. #11763186 | C22 | semidirect |
| 24. #11763185 | C22 | semidirect |
| 28. #11763157 | C22 | semidirect |
| 29. #11763156 | C22 | semidirect |
| 36. #11762531 | C22 | semidirect |
| 37. C8×#3622 | C22 | semidirect |
| 38. C17×#498 | C22 | semidirect |
| 41. C17×#486 | C22 | semidirect |
| 42. C17×#322 | C22 | semidirect |
| 172. C8×C17 | AGL(1,ℤ/8) | semidirect |
| 174. #3622 | AGL(1,ℤ/8) | semidirect |
| 182. #1715 | D17 | semidirect |
| 211. #498 | C2×D17 | semidirect |
| 226. #486 | C2×D17 | semidirect |
| 234. #322 | C2×D17 | semidirect |
| 289. C17 | #19745 | semidirect |
| 374. C8 | #10587600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539523 | 2 |
| #14539521 | 2 |
| #14539235 | 2 |
| #14539231 | 2 |
| #14528452 | 2 |
| #14528450 | 2 |
| #14528411 | 2 |
| #14528398 | 2 |
| #14528372 | 2 |
| #14527088 | 2 |
| C17×#1715 | 2 |
| #19745 | 17 |