Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
822 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 822 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. #14539527 | C2 | semidirect |
| 2. #14539501 | C2 | semidirect |
| 4. #14539155 | C2 | semidirect |
| 5. #14528456 | C2 | semidirect |
| 6. #14528434 | C2 | semidirect |
| 7. #14528420 | C2 | semidirect |
| 8. #14528410 | C2 | semidirect |
| 9. #14528385 | C2 | semidirect |
| 10. #14527086 | C2 | semidirect |
| 11. C17×#1709 | C2 | semidirect |
| 16. #11763212 | C22 | semidirect |
| 17. #11763207 | C22 | semidirect |
| 22. #11763181 | C22 | semidirect |
| 24. #11763160 | C22 | semidirect |
| 25. #11763159 | C22 | semidirect |
| 36. #11762530 | C22 | semidirect |
| 37. #11762530 | C22 | semidirect |
| 38. C17×#494 | C22 | semidirect |
| 41. C17×#486 | C22 | semidirect |
| 42. C82×C17 | C22 | semidirect |
| 173. #1709 | D17 | semidirect |
| 200. #494 | C2×D17 | semidirect |
| 213. #486 | C2×D17 | semidirect |
| 223. C82 | C2×D17 | semidirect |
| 275. C17 | #19749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539527 | 2 |
| #14539501 | 2 |
| #14539235 | 2 |
| #14539155 | 2 |
| #14528456 | 2 |
| #14528434 | 2 |
| #14528420 | 2 |
| #14528410 | 2 |
| #14528385 | 2 |
| #14527086 | 2 |
| C17×#1709 | 2 |
| #19749 | 17 |