Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 1. C2×#11763250 | C2 | semidirect |
| 3. #14537652 | C2 | semidirect |
| 4. #14530844 | C2 | semidirect |
| 5. #14530822 | C2 | semidirect |
| 6. #14530542 | C2 | semidirect |
| 7. #14530500 | C2 | semidirect |
| 8. #14530492 | C2 | semidirect |
| 9. C22×C17×SD32 | C2 | semidirect |
| 15. C2×#10587500 | C22 | semidirect |
| 16. C2×#10587499 | C22 | semidirect |
| 22. Q16×Dic17 | C22 | semidirect |
| 26. #11762627 | C22 | semidirect |
| 27. #11762614 | C22 | semidirect |
| 28. #11762611 | C22 | semidirect |
| 40. C2×Q16×C17 | D4 | semidirect |
| 158. C22×SD32 | D17 | semidirect |
| 220. C2×Q16 | C22⋊D17 | semidirect |
| 253. C17 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763250 | 2 |
| #14539265 | 2 |
| #14537652 | 2 |
| #14530844 | 2 |
| #14530822 | 2 |
| #14530542 | 2 |
| #14530500 | 2 |
| #14530492 | 2 |
| C22×C17×SD32 | 2 |
| #33587 | 17 |