Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 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×#22548762 | C2 | semidirect |
| 2. C22×#16860798 | C2 | semidirect |
| 3. #30632254 | C2 | semidirect |
| 4. #30631829 | C2 | semidirect |
| 5. #30631824 | C2 | semidirect |
| 6. #30631697 | C2 | semidirect |
| 7. #30631683 | C2 | semidirect |
| 8. #30631655 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C251 | C2 | semidirect |
| 15. C2×#16860809 | C22 | semidirect |
| 18. C2×Q8×D251 | C22 | semidirect |
| 27. #22548640 | C22 | semidirect |
| 28. #22548639 | C22 | semidirect |
| 29. #22548636 | C22 | semidirect |
| 30. (C2×D251)⋊C8 | C22 | semidirect |
| 48. C2×Dic502 | D4 | semidirect |
| 69. #41×C251 | D4 | semidirect |
| 145. C251 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D251 | semidirect |
| 191. #41 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548762 | 2 |
| C22×#16860798 | 2 |
| #30632254 | 2 |
| #30631829 | 2 |
| #30631824 | 2 |
| #30631697 | 2 |
| #30631683 | 2 |
| #30631655 | 2 |
| C2×AGL(1,ℤ/8)×C251 | 2 |
| #3010 | 251 |