Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 7. C22⋊(C251⋊C8) | C4 | semidirect |
| 13. C22⋊C8×C251 | C4 | semidirect |
| 71. C251 | #1306 | semidirect |
| 83. C22⋊C8 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631651 | 2 |
| #30631550 | 2 |
| #407×C251 | 2 |
| #1306 | 251 |