Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #30632053 | C2 | semidirect |
| 3. #30632049 | C2 | semidirect |
| 4. #30632044 | C2 | semidirect |
| 5. #30632035 | C2 | semidirect |
| 6. #30631691 | C2 | semidirect |
| 7. #30631686 | C2 | semidirect |
| 8. #30631681 | C2 | semidirect |
| 9. C2×#22548635 | C2 | semidirect |
| 10. #30631643 | C2 | semidirect |
| 11. #544×C251 | C2 | semidirect |
| 21. #22548638 | C22 | semidirect |
| 22. #22548638 | C22 | semidirect |
| 23. #22548638 | C22 | semidirect |
| 28. #22548635 | C22 | semidirect |
| 29. #22548635 | C22 | semidirect |
| 30. #22548635 | C22 | semidirect |
| 31. #22548626 | C22 | semidirect |
| 32. C4×C251⋊C8 | C22 | semidirect |
| 34. C4⋊Q8×C251 | C22 | semidirect |
| 36. #125×C251 | C22 | semidirect |
| 135. C251 | #3136 | semidirect |
| 137. #544 | D251 | semidirect |
| 153. C4⋊Q8 | C2×D251 | semidirect |
| 156. #125 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632256 | 2 |
| #30632053 | 2 |
| #30632049 | 2 |
| #30632044 | 2 |
| #30632035 | 2 |
| #30631691 | 2 |
| #30631686 | 2 |
| #30631681 | 2 |
| C2×#22548635 | 2 |
| #30631643 | 2 |
| #544×C251 | 2 |
| #3136 | 251 |