Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 171 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. #14539273 | C2 | semidirect |
| 3. #14537636 | C2 | semidirect |
| 4. #14530841 | C2 | semidirect |
| 5. #14530827 | C2 | semidirect |
| 6. #14530542 | C2 | semidirect |
| 7. #14530504 | C2 | semidirect |
| 8. #14530492 | C2 | semidirect |
| 9. C22×C17×SD32 | C2 | semidirect |
| 19. #11763194 | C22 | semidirect |
| 20. #11763187 | C22 | semidirect |
| 26. #11762627 | C22 | semidirect |
| 27. #11762614 | C22 | semidirect |
| 28. #11762613 | C22 | semidirect |
| 29. #11762611 | C22 | semidirect |
| 158. C22×SD32 | D17 | semidirect |
| 253. C17 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763245 | 2 |
| #14539273 | 2 |
| #14537636 | 2 |
| #14530841 | 2 |
| #14530827 | 2 |
| #14530542 | 2 |
| #14530504 | 2 |
| #14530492 | 2 |
| C22×C17×SD32 | 2 |
| #33586 | 17 |