Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #30632315 | C2 | semidirect |
| 3. #30632050 | C2 | semidirect |
| 4. #30632045 | C2 | semidirect |
| 5. #30632040 | C2 | semidirect |
| 6. #30632032 | C2 | semidirect |
| 7. #30631689 | C2 | semidirect |
| 8. #30631681 | C2 | semidirect |
| 9. C2×#22548636 | C2 | semidirect |
| 10. #30631645 | C2 | semidirect |
| 11. #418×C251 | C2 | semidirect |
| 15. #22548714 | C22 | semidirect |
| 18. #22548706 | C22 | semidirect |
| 26. #22548640 | C22 | semidirect |
| 27. #22548638 | C22 | semidirect |
| 28. #22548638 | C22 | semidirect |
| 29. #22548637 | C22 | semidirect |
| 32. #22548635 | C22 | semidirect |
| 33. #22548635 | C22 | semidirect |
| 34. #22548625 | C22 | semidirect |
| 35. C8×Dic251 | C22 | semidirect |
| 135. C251 | #3136 | semidirect |
| 143. #418 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632315 | 2 |
| #30632254 | 2 |
| #30632050 | 2 |
| #30632045 | 2 |
| #30632040 | 2 |
| #30632032 | 2 |
| #30631689 | 2 |
| #30631681 | 2 |
| C2×#22548636 | 2 |
| #30631645 | 2 |
| #418×C251 | 2 |
| #3136 | 251 |