Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 27. C251⋊C16 | Q8 | semidirect |
| 31. C16×C251 | Q8 | semidirect |
| 55. C251 | #2255 | semidirect |
| 87. C16 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632091 | 2 |
| #30632088 | 2 |
| #30631514 | 2 |
| #30631513 | 2 |
| #30631512 | 2 |
| #30631462 | 2 |
| #367×C251 | 2 |
| #2255 | 251 |