Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
240 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 12. #22548625 | C4 | semidirect |
| 13. C8×Dic251 | C4 | semidirect |
| 81. C251 | #1746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548625 | 2 |
| C2×C8×Dic251 | 2 |
| #30631533 | 2 |
| #30631442 | 2 |
| #30631441 | 2 |
| #336×C251 | 2 |
| #1746 | 251 |