Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30632397 | C2 | semidirect |
| 3. #30632034 | C2 | semidirect |
| 4. #30632007 | C2 | semidirect |
| 5. #30631977 | C2 | semidirect |
| 6. #30631919 | C2 | semidirect |
| 7. #30631887 | C2 | semidirect |
| 8. #30631836 | C2 | semidirect |
| 9. C8×D1004 | C2 | semidirect |
| 10. #102×D251 | C2 | semidirect |
| 11. C4×SD16×C251 | C2 | semidirect |
| 14. C2×#16860797 | C22 | semidirect |
| 15. C2×C8×D251 | C22 | semidirect |
| 16. #22548715 | C22 | semidirect |
| 20. #22548691 | C22 | semidirect |
| 26. C4⋊C4×D251 | C22 | semidirect |
| 27. #22548646 | C22 | semidirect |
| 28. C4⋊(C251⋊C8) | C22 | semidirect |
| 29. #22548637 | C22 | semidirect |
| 30. #22548637 | C22 | semidirect |
| 32. #22548635 | C22 | semidirect |
| 33. (C2×D251)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C251 | C22 | semidirect |
| 37. #106×C251 | C22 | semidirect |
| 38. #103×C251 | C22 | semidirect |
| 40. C4×C8×C251 | C22 | semidirect |
| 88. D1004 | SD16 | semidirect |
| 136. C251 | #3295 | semidirect |
| 146. C4×SD16 | D251 | semidirect |
| 162. C4×Q8 | C2×D251 | semidirect |
| 168. #106 | C2×D251 | semidirect |
| 170. #103 | C2×D251 | semidirect |
| 177. C4×C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632397 | 2 |
| D4×D1004 | 2 |
| #30632034 | 2 |
| #30632007 | 2 |
| #30631977 | 2 |
| #30631919 | 2 |
| #30631887 | 2 |
| #30631836 | 2 |
| C8×D1004 | 2 |
| #102×D251 | 2 |
| C4×SD16×C251 | 2 |
| #3295 | 251 |