Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #30632035 | C2 | semidirect |
| 3. #30632005 | C2 | semidirect |
| 4. #30631974 | C2 | semidirect |
| 5. #30631918 | C2 | semidirect |
| 6. #30631887 | C2 | semidirect |
| 7. #30631837 | C2 | semidirect |
| 8. C4×#16860797 | C2 | semidirect |
| 9. D4×C251⋊C8 | C2 | semidirect |
| 10. C2×#22548635 | C2 | semidirect |
| 11. #554×C251 | C2 | semidirect |
| 15. C2×#16860797 | C22 | semidirect |
| 16. C22×C251⋊C8 | C22 | semidirect |
| 22. #22548646 | C22 | semidirect |
| 23. #22548646 | C22 | semidirect |
| 24. C4⋊(C251⋊C8) | C22 | semidirect |
| 25. #22548639 | C22 | semidirect |
| 28. #22548635 | C22 | semidirect |
| 29. #22548635 | C22 | semidirect |
| 30. #22548635 | C22 | semidirect |
| 31. C22⋊(C251⋊C8) | C22 | semidirect |
| 32. C4×C251⋊C8 | C22 | semidirect |
| 33. C4⋊Q8×C251 | C22 | semidirect |
| 36. C22⋊Q8×C251 | C22 | semidirect |
| 37. C4×Q8×C251 | C22 | semidirect |
| 40. C2×C4⋊C4×C251 | C22 | semidirect |
| 99. D4×C251 | SD16 | semidirect |
| 136. C251 | #3295 | semidirect |
| 138. #554 | D251 | semidirect |
| 154. C4⋊Q8 | C2×D251 | semidirect |
| 158. C22⋊Q8 | C2×D251 | semidirect |
| 162. C4×Q8 | C2×D251 | semidirect |
| 166. C2×C4⋊C4 | C2×D251 | semidirect |
| 231. D4 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D1004 | 2 |
| #30632035 | 2 |
| #30632005 | 2 |
| #30631974 | 2 |
| #30631918 | 2 |
| #30631887 | 2 |
| #30631837 | 2 |
| C4×#16860797 | 2 |
| D4×C251⋊C8 | 2 |
| C2×#22548635 | 2 |
| #554×C251 | 2 |
| #3295 | 251 |