Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
292 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 53. C4×C251 | #101 | semidirect |
| 61. C251 | #1966 | semidirect |
| 116. C4 | #22548633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548715 | 2 |
| C2×#22548633 | 2 |
| C4×#16860794 | 2 |
| #423×C251 | 2 |
| #1966 | 251 |