Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#22548740 | C2 | semidirect |
| 2. C2×#22548722 | C2 | semidirect |
| 3. #30632251 | C2 | semidirect |
| 4. #30631938 | C2 | semidirect |
| 5. #30631935 | C2 | semidirect |
| 6. #30631921 | C2 | semidirect |
| 7. #30631918 | C2 | semidirect |
| 8. #30631727 | C2 | semidirect |
| 9. #30631683 | C2 | semidirect |
| 10. C2×#22548635 | C2 | semidirect |
| 11. #537×C251 | C2 | semidirect |
| 18. C2×#16860794 | C22 | semidirect |
| 20. C22×C251⋊C8 | C22 | semidirect |
| 27. #22548648 | C22 | semidirect |
| 28. #22548646 | C22 | semidirect |
| 29. #22548639 | C22 | semidirect |
| 30. #22548639 | C22 | semidirect |
| 31. #22548636 | C22 | semidirect |
| 32. #22548636 | C22 | semidirect |
| 38. C22⋊Q8×C251 | C22 | semidirect |
| 41. #121×C251 | C22 | semidirect |
| 53. #16860794 | D4 | semidirect |
| 151. C251 | #3062 | semidirect |
| 155. #537 | D251 | semidirect |
| 178. C22⋊Q8 | C2×D251 | semidirect |
| 183. #121 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| C2×#22548722 | 2 |
| #30632251 | 2 |
| #30631938 | 2 |
| #30631935 | 2 |
| #30631921 | 2 |
| #30631918 | 2 |
| #30631727 | 2 |
| #30631683 | 2 |
| C2×#22548635 | 2 |
| #537×C251 | 2 |
| #3062 | 251 |