Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 8. C22⋊(C251⋊C8) | C4 | semidirect |
| 11. C2×M16×C251 | C4 | semidirect |
| 76. C251 | #1305 | semidirect |
| 83. C2×M16 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631651 | 2 |
| #30631547 | 2 |
| #407×C251 | 2 |
| #1305 | 251 |