Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. #30632341 | C2 | semidirect |
| 2. #30632033 | C2 | semidirect |
| 3. #30631998 | C2 | semidirect |
| 4. #30631967 | C2 | semidirect |
| 5. #30631921 | C2 | semidirect |
| 6. #30631879 | C2 | semidirect |
| 7. #30631821 | C2 | semidirect |
| 8. C4×#16860795 | C2 | semidirect |
| 9. D4×C251⋊C8 | C2 | semidirect |
| 10. C2×#22548636 | C2 | semidirect |
| 11. D42×C251 | C2 | semidirect |
| 14. C2×#16860795 | C22 | semidirect |
| 15. C22×C251⋊C8 | C22 | semidirect |
| 16. #22548715 | C22 | semidirect |
| 19. #22548689 | C22 | semidirect |
| 20. C4×D1004 | C22 | semidirect |
| 21. C2×C4⋊Dic251 | C22 | semidirect |
| 22. #22548648 | C22 | semidirect |
| 23. #22548648 | C22 | semidirect |
| 24. C4⋊(C251⋊C8) | C22 | semidirect |
| 27. #22548636 | C22 | semidirect |
| 28. #22548636 | C22 | semidirect |
| 29. #22548636 | C22 | semidirect |
| 30. #22548635 | C22 | semidirect |
| 31. C22⋊(C251⋊C8) | C22 | semidirect |
| 32. C4×C251⋊C8 | C22 | semidirect |
| 103. D4×C251 | D8 | semidirect |
| 104. D4×C251 | #41 | semidirect |
| 142. C251 | #3294 | semidirect |
| 145. D42 | D251 | semidirect |
| 239. D4 | #16860795 | semidirect |
| 240. D4 | #16860809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632341 | 2 |
| #30632033 | 2 |
| #30631998 | 2 |
| #30631967 | 2 |
| #30631921 | 2 |
| #30631879 | 2 |
| #30631821 | 2 |
| C4×#16860795 | 2 |
| D4×C251⋊C8 | 2 |
| C2×#22548636 | 2 |
| D42×C251 | 2 |
| #3294 | 251 |