Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #30631984 | C2 | semidirect |
| 3. #30631984 | C2 | semidirect |
| 4. #30631974 | C2 | semidirect |
| 5. #30631964 | C2 | semidirect |
| 6. #30631727 | C2 | semidirect |
| 7. #30631723 | C2 | semidirect |
| 8. #30631714 | C2 | semidirect |
| 11. #544×C251 | C2 | semidirect |
| 21. #22548648 | C22 | semidirect |
| 22. #22548648 | C22 | semidirect |
| 23. #22548648 | C22 | semidirect |
| 24. #22548646 | C22 | semidirect |
| 25. #22548646 | C22 | semidirect |
| 26. #22548646 | C22 | semidirect |
| 27. C4⋊(C251⋊C8) | C22 | semidirect |
| 28. C4⋊(C251⋊C8) | C22 | semidirect |
| 34. C4⋊Q8×C251 | C22 | semidirect |
| 36. #125×C251 | C22 | semidirect |
| 44. C2×D1004 | Q8 | semidirect |
| 124. C251 | #3081 | semidirect |
| 126. #544 | D251 | semidirect |
| 141. C4⋊Q8 | C2×D251 | semidirect |
| 143. #125 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632161 | 2 |
| #30631984 | 2 |
| #30631974 | 2 |
| #30631964 | 2 |
| #30631727 | 2 |
| #30631723 | 2 |
| #30631714 | 2 |
| #30631691 | 2 |
| C2×#22548635 | 2 |
| #544×C251 | 2 |
| #3081 | 251 |