Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
712 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#11763243 | C2 | semidirect |
| 2. #14540470 | C2 | semidirect |
| 3. #14531045 | C2 | semidirect |
| 4. #14530898 | C2 | semidirect |
| 5. #14530839 | C2 | semidirect |
| 6. #14530725 | C2 | semidirect |
| 7. #14530697 | C2 | semidirect |
| 8. #14530617 | C2 | semidirect |
| 9. C4×C17×D16 | C2 | semidirect |
| 11. C2×D8×D17 | C22 | semidirect |
| 14. C2×Dic136 | C22 | semidirect |
| 15. C2×#10587471 | C22 | semidirect |
| 16. C2×#10587498 | C22 | semidirect |
| 19. C2×#10587469 | C22 | semidirect |
| 20. #11763193 | C22 | semidirect |
| 21. #11763051 | C22 | semidirect |
| 27. C4⋊#63214 | C22 | semidirect |
| 28. #11762612 | C22 | semidirect |
| 29. #11762609 | C22 | semidirect |
| 30. #11762588 | C22 | semidirect |
| 32. C4×D8×C17 | C22 | semidirect |
| 33. C17×#366 | C22 | semidirect |
| 34. C17×#357 | C22 | semidirect |
| 35. C4×C16×C17 | C22 | semidirect |
| 58. C17×D16 | D4 | semidirect |
| 155. C4×D16 | D17 | semidirect |
| 192. C4×D8 | C2×D17 | semidirect |
| 194. #366 | C2×D17 | semidirect |
| 198. #357 | C2×D17 | semidirect |
| 200. C4×C16 | C2×D17 | semidirect |
| 234. D16 | D68 | semidirect |
| 246. C17 | #33839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763243 | 2 |
| #14540470 | 2 |
| #14531045 | 2 |
| #14530898 | 2 |
| #14530839 | 2 |
| #14530725 | 2 |
| #14530697 | 2 |
| #14530617 | 2 |
| C4×C17×D16 | 2 |
| #33839 | 17 |