Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #30632504 | C2 | semidirect |
| 2. #30632497 | C2 | semidirect |
| 3. #30632488 | C2 | semidirect |
| 4. #30632070 | C2 | semidirect |
| 5. #30631963 | C2 | semidirect |
| 6. #30631949 | C2 | semidirect |
| 7. #30631867 | C2 | semidirect |
| 8. #30631858 | C2 | semidirect |
| 9. #30631803 | C2 | semidirect |
| 10. #30631802 | C2 | semidirect |
| 11. #472×C251 | C2 | semidirect |
| 12. #22548762 | C22 | semidirect |
| 16. #22548748 | C22 | semidirect |
| 27. C2×Dic1004 | C22 | semidirect |
| 28. C2×#16860798 | C22 | semidirect |
| 31. #22548723 | C22 | semidirect |
| 33. #22548702 | C22 | semidirect |
| 34. #22548650 | C22 | semidirect |
| 35. #22548642 | C22 | semidirect |
| 37. #22548641 | C22 | semidirect |
| 38. #22548633 | C22 | semidirect |
| 39. C8×Dic251 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C251 | C22 | semidirect |
| 42. #131×C251 | C22 | semidirect |
| 43. #108×C251 | C22 | semidirect |
| 44. #100×C251 | C22 | semidirect |
| 149. C251 | #3290 | semidirect |
| 156. #472 | D251 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D251 | semidirect |
| 185. #131 | C2×D251 | semidirect |
| 188. #108 | C2×D251 | semidirect |
| 193. #100 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632504 | 2 |
| #30632497 | 2 |
| #30632488 | 2 |
| #30632070 | 2 |
| #30631963 | 2 |
| #30631949 | 2 |
| #30631867 | 2 |
| #30631858 | 2 |
| #30631803 | 2 |
| #30631802 | 2 |
| #472×C251 | 2 |
| #3290 | 251 |