Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#16860800 | C2 | semidirect |
| 2. C22×#16860799 | C2 | semidirect |
| 4. C2×#22548704 | C2 | semidirect |
| 5. C2×#22548702 | C2 | semidirect |
| 6. #30632068 | C2 | direct (N × H) |
| 7. C2×C8×Dic251 | C2 | semidirect |
| 8. C22×SD16×C251 | C2 | semidirect |
| 12. C2×#16860800 | C22 | semidirect |
| 14. C2×#16860799 | C22 | semidirect |
| 19. #22548704 | C22 | semidirect |
| 21. #22548702 | C22 | semidirect |
| 25. C8×Dic251 | C22 | semidirect |
| 29. C2×SD16×C251 | C22 | semidirect |
| 112. C2×C251 | #495 | semidirect |
| 116. C251 | C2×#495 | semidirect |
| 120. C22×SD16 | D251 | semidirect |
| 135. C2×SD16 | C2×D251 | semidirect |
| 230. C2 | #30632068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860800 | 2 |
| C22×#16860799 | 2 |
| C22×#16860795 | 2 |
| C2×#22548704 | 2 |
| C2×#22548702 | 2 |
| #30632068 | 2 |
| C2×C8×Dic251 | 2 |
| C22×SD16×C251 | 2 |
| C2×#495 | 251 |