Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 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 |
|---|---|---|
| 2. C22×#16860800 | C2 | semidirect |
| 3. C2×#22548691 | C2 | semidirect |
| 4. #30631846 | C2 | direct (N × H) |
| 5. C2×#22548640 | C2 | semidirect |
| 6. C2×#22548636 | C2 | semidirect |
| 7. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 8. C22×SD16×C251 | C2 | semidirect |
| 18. C2×#16860800 | C22 | semidirect |
| 21. #22548691 | C22 | semidirect |
| 25. #22548640 | C22 | semidirect |
| 26. #22548636 | C22 | semidirect |
| 27. (C2×D251)⋊C8 | C22 | semidirect |
| 31. C2×SD16×C251 | C22 | semidirect |
| 130. C2×C251 | #452 | semidirect |
| 135. C251 | C2×#452 | semidirect |
| 139. C22×SD16 | D251 | semidirect |
| 158. C2×SD16 | C2×D251 | semidirect |
| 267. C2 | #30631846 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860809 | 2 |
| C22×#16860800 | 2 |
| C2×#22548691 | 2 |
| #30631846 | 2 |
| C2×#22548640 | 2 |
| C2×#22548636 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C22×SD16×C251 | 2 |
| C2×#452 | 251 |