Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
806 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 153 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×#22548741 | C2 | semidirect |
| 3. #30631830 | C2 | semidirect |
| 4. #30631825 | C2 | semidirect |
| 5. #30631820 | C2 | semidirect |
| 6. #30631686 | C2 | semidirect |
| 7. #30631651 | C2 | semidirect |
| 8. C2×#121×C251 | C2 | semidirect |
| 13. C2×#16860810 | C22 | semidirect |
| 14. C22×Dic502 | C22 | semidirect |
| 15. C22×D1004 | C22 | semidirect |
| 19. C2×#16860798 | C22 | semidirect |
| 20. C2×#16860795 | C22 | semidirect |
| 21. C2×#16860794 | C22 | semidirect |
| 22. #22548638 | C22 | semidirect |
| 23. #22548635 | C22 | semidirect |
| 24. C22⋊(C251⋊C8) | C22 | semidirect |
| 25. C22⋊(C251⋊C8) | C22 | semidirect |
| 27. C22×D4×C251 | C22 | semidirect |
| 32. #121×C251 | C22 | semidirect |
| 33. C2×C4⋊C4×C251 | C22 | semidirect |
| 41. #16860810 | D4 | semidirect |
| 85. Dic502 | C2×D4 | semidirect |
| 88. D1004 | C2×D4 | semidirect |
| 135. C22×C251 | AGL(1,ℤ/8) | semidirect |
| 155. C251 | #3006 | semidirect |
| 159. C2×#121 | D251 | semidirect |
| 174. C22×D4 | C2×D251 | semidirect |
| 184. #121 | C2×D251 | semidirect |
| 185. C2×C4⋊C4 | C2×D251 | semidirect |
| 295. C22 | #22548741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860810 | 2 |
| C2×#22548741 | 2 |
| #30631830 | 2 |
| #30631825 | 2 |
| #30631820 | 2 |
| #30631686 | 2 |
| #30631651 | 2 |
| C2×#121×C251 | 2 |
| #3006 | 251 |