Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #30632232 | C2 | semidirect |
| 2. C2×D4×Dic251 | C2 | semidirect |
| 3. #30632006 | C2 | semidirect |
| 4. #30632003 | C2 | semidirect |
| 5. #30631975 | C2 | semidirect |
| 6. #30631880 | C2 | semidirect |
| 7. #30631821 | C2 | semidirect |
| 8. #30631799 | C2 | semidirect |
| 9. #30631796 | C2 | semidirect |
| 10. #30631741 | C2 | semidirect |
| 11. #447×C251 | C2 | semidirect |
| 15. #22548714 | C22 | semidirect |
| 16. #22548711 | C22 | semidirect |
| 24. D4×Dic251 | C22 | semidirect |
| 25. #22548677 | C22 | semidirect |
| 30. #22548647 | C22 | semidirect |
| 31. #22548646 | C22 | semidirect |
| 32. Dic251⋊C8 | C22 | semidirect |
| 33. #22548637 | C22 | semidirect |
| 35. #22548636 | C22 | semidirect |
| 37. #22548625 | C22 | semidirect |
| 113. D4×C251 | #41 | semidirect |
| 149. C251 | #3109 | semidirect |
| 158. #447 | D251 | semidirect |
| 249. D4 | #16860809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632232 | 2 |
| C2×D4×Dic251 | 2 |
| #30632006 | 2 |
| #30632003 | 2 |
| #30631975 | 2 |
| #30631880 | 2 |
| #30631821 | 2 |
| #30631799 | 2 |
| #30631796 | 2 |
| #30631741 | 2 |
| #447×C251 | 2 |
| #3109 | 251 |