Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×Dic251⋊C4 | C4 | semidirect |
| 11. C2×C4×Dic251 | C4 | semidirect |
| 78. C251 | #1820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548671 | 2 |
| #30631548 | 2 |
| #30631454 | 2 |
| #30631453 | 2 |
| #342×C251 | 2 |
| #1820 | 251 |