Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #30631642 | C2 | semidirect |
| 4. C2×#22548625 | C2 | semidirect |
| 5. #30631451 | C2 | semidirect |
| 6. #30631448 | C2 | semidirect |
| 12. #22548642 | C4 | semidirect |
| 13. #22548639 | C4 | semidirect |
| 14. #22548636 | C4 | semidirect |
| 20. #131×C251 | C4 | semidirect |
| 98. C251 | #1765 | semidirect |
| 109. #131 | Dic251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548642 | 2 |
| #30631683 | 2 |
| #30631642 | 2 |
| C2×#22548625 | 2 |
| #30631451 | 2 |
| #30631448 | 2 |
| C2×#131×C251 | 2 |
| #1765 | 251 |