Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
774 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 255 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×#22548722 | C2 | semidirect |
| 3. #30631655 | C2 | semidirect |
| 4. #30631653 | C2 | semidirect |
| 5. #30631650 | C2 | semidirect |
| 6. C2×(C2×D251)⋊C8 | C2 | semidirect |
| 7. C2×#131×C251 | C2 | semidirect |
| 17. C2×#16860794 | C22 | semidirect |
| 18. C22×C251⋊C8 | C22 | semidirect |
| 21. (C2×D251)⋊C8 | C22 | semidirect |
| 22. (C2×D251)⋊C8 | C22 | semidirect |
| 23. (C2×D251)⋊C8 | C22 | semidirect |
| 26. C2×M16×C251 | C22 | semidirect |
| 27. C22×C8×C251 | C22 | semidirect |
| 96. C2×D251 | #131 | semidirect |
| 108. C251 | #2880 | semidirect |
| 112. C2×#131 | D251 | semidirect |
| 129. C2×M16 | C2×D251 | semidirect |
| 131. C22×C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×D251 | 2 |
| C2×#22548722 | 2 |
| #30631655 | 2 |
| #30631653 | 2 |
| #30631650 | 2 |
| C2×(C2×D251)⋊C8 | 2 |
| C2×#131×C251 | 2 |
| #2880 | 251 |