Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #30632161 | C2 | semidirect |
| 3. #30631798 | C2 | semidirect |
| 4. #30631769 | C2 | semidirect |
| 5. #30631691 | C2 | semidirect |
| 6. #30631642 | C2 | semidirect |
| 7. #427×C251 | C2 | semidirect |
| 9. C2×D2008 | C4 | semidirect |
| 14. #22548677 | C22 | semidirect |
| 17. #22548635 | C22 | semidirect |
| 18. #22548625 | C22 | semidirect |
| 19. C8×Dic251 | C22 | semidirect |
| 22. #107×C251 | C22 | semidirect |
| 23. #106×C251 | C22 | semidirect |
| 27. C2×D1004 | C2×C4 | semidirect |
| 30. D2008 | C2×C4 | semidirect |
| 31. D2008 | C2×C4 | semidirect |
| 39. C2×C8×C251 | C2×C4 | semidirect |
| 77. C251 | #2948 | semidirect |
| 83. #427 | D251 | semidirect |
| 97. #107 | C2×D251 | semidirect |
| 98. #106 | C2×D251 | semidirect |
| 113. C2×C8 | C4×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2008 | 2 |
| #30632161 | 2 |
| #30631798 | 2 |
| #30631769 | 2 |
| #30631691 | 2 |
| #30631642 | 2 |
| #427×C251 | 2 |
| #2948 | 251 |