Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #14539443 | C2 | semidirect |
| 3. #14531004 | C2 | semidirect |
| 4. #14530961 | C2 | semidirect |
| 5. #14530866 | C2 | semidirect |
| 7. #14530677 | C2 | semidirect |
| 8. C17×#2166 | C2 | semidirect |
| 13. #11763211 | C22 | semidirect |
| 14. #11763189 | C22 | semidirect |
| 22. #11762917 | C22 | semidirect |
| 26. #11762632 | C22 | semidirect |
| 27. #11762626 | C22 | semidirect |
| 30. C17×#364 | C22 | semidirect |
| 32. C17×#347 | C22 | semidirect |
| 151. #2166 | D17 | semidirect |
| 184. #364 | C2×D17 | semidirect |
| 188. #347 | C2×D17 | semidirect |
| 231. C17 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539443 | 2 |
| #14537688 | 2 |
| #14531004 | 2 |
| #14530961 | 2 |
| #14530866 | 2 |
| #14530737 | 2 |
| #14530677 | 2 |
| C17×#2166 | 2 |
| #33693 | 17 |