Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 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 |
|---|---|---|
| 1. C2×#22548761 | C2 | semidirect |
| 2. C22×#16860795 | C2 | semidirect |
| 3. #30632254 | C2 | semidirect |
| 4. #30631831 | C2 | semidirect |
| 5. #30631819 | C2 | semidirect |
| 6. #30631693 | C2 | semidirect |
| 7. #30631683 | C2 | semidirect |
| 8. #30631655 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C251 | C2 | semidirect |
| 12. C2×#16860811 | C22 | semidirect |
| 18. C2×D4×D251 | C22 | semidirect |
| 20. C2×#16860795 | C22 | semidirect |
| 21. C22×C251⋊C8 | C22 | semidirect |
| 24. #22548686 | C22 | semidirect |
| 26. #22548674 | C22 | semidirect |
| 27. #22548639 | C22 | semidirect |
| 28. #22548637 | C22 | semidirect |
| 29. #22548636 | C22 | semidirect |
| 30. (C2×D251)⋊C8 | C22 | semidirect |
| 32. C22×D4×C251 | C22 | semidirect |
| 34. C2×SD16×C251 | C22 | semidirect |
| 35. C2×D8×C251 | C22 | semidirect |
| 36. C2×M16×C251 | C22 | semidirect |
| 50. C2×D1004 | D4 | semidirect |
| 69. #41×C251 | D4 | semidirect |
| 151. C251 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D251 | semidirect |
| 172. C22×D4 | C2×D251 | semidirect |
| 174. C2×SD16 | C2×D251 | semidirect |
| 177. C2×D8 | C2×D251 | semidirect |
| 178. C2×M16 | C2×D251 | semidirect |
| 198. #41 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548761 | 2 |
| C22×#16860795 | 2 |
| #30632254 | 2 |
| #30631831 | 2 |
| #30631819 | 2 |
| #30631693 | 2 |
| #30631683 | 2 |
| #30631655 | 2 |
| C2×AGL(1,ℤ/8)×C251 | 2 |
| #3008 | 251 |