Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #30631464 | C2 | semidirect |
| 7. #22548655 | C4 | semidirect |
| 9. C2×C251⋊C16 | C4 | semidirect |
| 13. M32×C251 | C4 | semidirect |
| 15. C2×C16×C251 | C4 | semidirect |
| 57. C251 | #2110 | semidirect |
| 68. M32 | Dic251 | semidirect |
| 71. C2×C16 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548655 | 2 |
| #30631642 | 2 |
| #30631464 | 2 |
| C2×M32×C251 | 2 |
| #2110 | 251 |