Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 194 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 |
|---|---|---|
| 2. #30632037 | C2 | semidirect |
| 4. #30631432 | C2 | semidirect |
| 5. Q8⋊(C251⋊C8) | C2 | semidirect |
| 7. #477×C251 | C2 | semidirect |
| 86. C251 | #1638 | semidirect |
| 90. #477 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632410 | 2 |
| #30632037 | 2 |
| #30631974 | 2 |
| #30631432 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| #30631414 | 2 |
| #477×C251 | 2 |
| #1638 | 251 |