Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22548748 | C2 | semidirect |
| 3. C22×#16860800 | C2 | semidirect |
| 4. #30632263 | C2 | semidirect |
| 5. #30631852 | C2 | semidirect |
| 6. #30631844 | C2 | semidirect |
| 7. #30631681 | C2 | semidirect |
| 8. #30631655 | C2 | semidirect |
| 9. #419×C251 | C2 | semidirect |
| 140. C251 | #3011 | semidirect |
| 148. #419 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548763 | 2 |
| C2×#22548748 | 2 |
| C22×#16860800 | 2 |
| #30632263 | 2 |
| #30631852 | 2 |
| #30631844 | 2 |
| #30631681 | 2 |
| #30631655 | 2 |
| #419×C251 | 2 |
| #3011 | 251 |