Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 19. #106×C251 | C4 | semidirect |
| 96. C251 | #1920 | semidirect |
| 114. #106 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30631586 | 2 |
| C4⋊C4×Dic251 | 2 |
| #30631450 | 2 |
| #30631449 | 2 |
| #30631441 | 2 |
| C2×#106×C251 | 2 |
| #1920 | 251 |