Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 565 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. C22×#16860810 | C2 | semidirect |
| 2. C2×#22548735 | C2 | direct (N × H) |
| 3. C22×#16860800 | C2 | semidirect |
| 4. C22×#16860798 | C2 | semidirect |
| 5. C22×#16860797 | C2 | semidirect |
| 6. C22×#16860795 | C2 | semidirect |
| 7. C23×C251⋊C8 | C2 | semidirect |
| 8. C22×#41×C251 | C2 | semidirect |
| 10. C2×#16860810 | C22 | semidirect |
| 15. #22548735 | C22 | direct (N × H) |
| 16. C2×#16860800 | C22 | semidirect |
| 17. C2×#16860798 | C22 | semidirect |
| 18. C2×#16860797 | C22 | semidirect |
| 19. C2×#16860795 | C22 | semidirect |
| 22. C22×C251⋊C8 | C22 | semidirect |
| 24. C2×#41×C251 | C22 | semidirect |
| 32. #16860810 | C23 | semidirect |
| 40. #16860800 | C23 | semidirect |
| 41. #16860798 | C23 | semidirect |
| 42. #16860797 | C23 | semidirect |
| 43. #16860795 | C23 | semidirect |
| 46. C2×C251⋊C8 | C23 | semidirect |
| 50. #41×C251 | C23 | semidirect |
| 93. C22×C251 | #135 | semidirect |
| 105. C2×C251 | C2×#135 | semidirect |
| 108. C251 | C22×#135 | semidirect |
| 111. C22×#41 | D251 | semidirect |
| 121. C2×#41 | C2×D251 | semidirect |
| 145. #41 | C22×D251 | semidirect |
| 204. C22 | #22548735 | direct (N × H) |
| 215. C2 | C2×#22548735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C2×#22548735 | 2 |
| C22×#16860800 | 2 |
| C22×#16860798 | 2 |
| C22×#16860797 | 2 |
| C22×#16860795 | 2 |
| C23×C251⋊C8 | 2 |
| C22×#41×C251 | 2 |
| C22×#135 | 251 |