Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 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. D17×#499 | C2 | semidirect |
| 3. #14531027 | C2 | semidirect |
| 4. #14531026 | C2 | semidirect |
| 5. #14531025 | C2 | semidirect |
| 6. #14531024 | C2 | semidirect |
| 7. D17×#357 | C2 | semidirect |
| 8. D17×#346 | C2 | semidirect |
| 9. C17×#2244 | C2 | semidirect |
| 15. #11763211 | C22 | semidirect |
| 16. #11763210 | C22 | semidirect |
| 26. #11762611 | C22 | semidirect |
| 27. #11762610 | C22 | semidirect |
| 28. #11762609 | C22 | semidirect |
| 29. #11762585 | C22 | semidirect |
| 30. #11762584 | C22 | semidirect |
| 31. C17×#499 | C22 | semidirect |
| 33. C17×#357 | C22 | semidirect |
| 34. C17×#346 | C22 | semidirect |
| 142. #2244 | D17 | direct (N × H) |
| 169. #499 | C2×D17 | semidirect |
| 181. #357 | C2×D17 | semidirect |
| 184. #346 | C2×D17 | semidirect |
| 189. D17 | #2244 | direct (N × H) |
| 226. C17 | C2×#2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17×#499 | 2 |
| D17×#493 | 2 |
| #14531027 | 2 |
| #14531026 | 2 |
| #14531025 | 2 |
| #14531024 | 2 |
| D17×#357 | 2 |
| D17×#346 | 2 |
| C17×#2244 | 2 |
| C2×#2244 | 17 |