Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
144 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 69. C251 | #1684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632039 | 2 |
| #30631972 | 2 |
| Q8×C251⋊C8 | 2 |
| #30631439 | 2 |
| #30631436 | 2 |
| #30631432 | 2 |
| #477×C251 | 2 |
| #1684 | 251 |