Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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. #30632454 | C2 | semidirect |
| 3. #30631691 | C2 | semidirect |
| 4. C2×#22548631 | C2 | semidirect |
| 5. #30631457 | C2 | semidirect |
| 6. C251⋊#338 | C2 | semidirect |
| 7. #421×C251 | C2 | semidirect |
| 11. C2×#16860797 | C4 | semidirect |
| 12. C2×#16860795 | C4 | semidirect |
| 112. C251 | #1903 | semidirect |
| 116. #421 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| #30632454 | 2 |
| #30631691 | 2 |
| C2×#22548631 | 2 |
| #30631457 | 2 |
| C251⋊#338 | 2 |
| #421×C251 | 2 |
| #1903 | 251 |