Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#22548741 | C2 | semidirect |
| 2. #30632254 | C2 | semidirect |
| 3. #30632162 | C2 | semidirect |
| 4. #30631900 | C2 | semidirect |
| 5. #30631880 | C2 | semidirect |
| 6. #30631713 | C2 | semidirect |
| 7. #30631692 | C2 | semidirect |
| 8. #30631684 | C2 | semidirect |
| 9. C22×D8×C251 | C2 | semidirect |
| 12. C2×#16860798 | C22 | semidirect |
| 13. C2×#16860795 | C22 | semidirect |
| 15. #22548711 | C22 | semidirect |
| 16. #22548702 | C22 | semidirect |
| 20. D4×Dic251 | C22 | semidirect |
| 24. Dic251⋊C8 | C22 | semidirect |
| 25. #22548640 | C22 | semidirect |
| 26. #22548637 | C22 | semidirect |
| 27. #22548636 | C22 | semidirect |
| 60. C2×D4×C251 | D4 | semidirect |
| 121. C251 | #3041 | semidirect |
| 124. C22×D8 | D251 | semidirect |
| 168. C2×D4 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548741 | 2 |
| #30632254 | 2 |
| #30632162 | 2 |
| #30631900 | 2 |
| #30631880 | 2 |
| #30631713 | 2 |
| #30631692 | 2 |
| #30631684 | 2 |
| C22×D8×C251 | 2 |
| #3041 | 251 |