Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
446 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#22548748 | C2 | semidirect |
| 3. C2×#22548745 | C2 | semidirect |
| 4. #30631962 | C2 | semidirect |
| 5. #30631950 | C2 | semidirect |
| 6. #30631736 | C2 | semidirect |
| 7. #30631669 | C2 | semidirect |
| 8. C2×#22548633 | C2 | semidirect |
| 9. #568×C251 | C2 | semidirect |
| 21. C2×Dic1004 | C22 | semidirect |
| 23. C2×#16860799 | C22 | semidirect |
| 27. #22548651 | C22 | semidirect |
| 28. #22548633 | C22 | semidirect |
| 29. #22548633 | C22 | semidirect |
| 30. #22548631 | C22 | semidirect |
| 142. C251 | #3069 | semidirect |
| 147. #568 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632485 | 2 |
| C2×#22548748 | 2 |
| C2×#22548745 | 2 |
| #30631962 | 2 |
| #30631950 | 2 |
| #30631736 | 2 |
| #30631669 | 2 |
| C2×#22548633 | 2 |
| #568×C251 | 2 |
| #3069 | 251 |