Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #30632015 | C2 | semidirect |
| 3. #30631974 | C2 | semidirect |
| 4. #30631889 | C2 | semidirect |
| 6. C4×#16860797 | C2 | semidirect |
| 7. #30631740 | C2 | semidirect |
| 8. #533×C251 | C2 | semidirect |
| 18. #22548646 | C22 | semidirect |
| 19. C4⋊(C251⋊C8) | C22 | semidirect |
| 20. #22548639 | C22 | semidirect |
| 23. C4×C251⋊C8 | C22 | semidirect |
| 24. C4⋊Q8×C251 | C22 | semidirect |
| 25. C4⋊Q8×C251 | C22 | semidirect |
| 30. C4×Q8×C251 | C22 | semidirect |
| 83. C2×C4×C251 | SD16 | semidirect |
| 112. C251 | #3101 | semidirect |
| 114. #533 | D251 | semidirect |
| 125. C4⋊Q8 | C2×D251 | semidirect |
| 126. C4⋊Q8 | C2×D251 | semidirect |
| 131. C4×Q8 | C2×D251 | semidirect |
| 195. C2×C4 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1004 | 2 |
| #30632015 | 2 |
| #30631974 | 2 |
| #30631889 | 2 |
| #30631837 | 2 |
| C4×#16860797 | 2 |
| #30631740 | 2 |
| #533×C251 | 2 |
| #3101 | 251 |