Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
642 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 2. #14537700 | C2 | semidirect |
| 3. #14530669 | C2 | semidirect |
| 4. #14530664 | C2 | semidirect |
| 5. C2×#11762615 | C2 | semidirect |
| 6. #14530383 | C2 | semidirect |
| 7. C17×#2161 | C2 | semidirect |
| 10. #11763252 | C4 | semidirect |
| 11. #11763247 | C4 | semidirect |
| 15. #11762925 | C22 | semidirect |
| 18. #11762615 | C22 | semidirect |
| 19. #11762615 | C22 | semidirect |
| 20. #11762584 | C22 | semidirect |
| 21. C16×Dic17 | C22 | semidirect |
| 24. C17×#368 | C22 | semidirect |
| 111. #2161 | D17 | semidirect |
| 136. #368 | C2×D17 | semidirect |
| 173. C17 | #33464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541920 | 2 |
| #14537700 | 2 |
| #14530669 | 2 |
| #14530664 | 2 |
| C2×#11762615 | 2 |
| #14530383 | 2 |
| C17×#2161 | 2 |
| #33464 | 17 |