Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 1. #30632170 | C2 | semidirect |
| 2. #30632008 | C2 | semidirect |
| 3. #30632008 | C2 | semidirect |
| 4. #30632003 | C2 | semidirect |
| 5. #30631998 | C2 | semidirect |
| 6. #30631730 | C2 | semidirect |
| 7. #30631723 | C2 | semidirect |
| 8. #30631692 | C2 | semidirect |
| 9. C2×#22548636 | C2 | semidirect |
| 10. #30631654 | C2 | semidirect |
| 18. #22548674 | C22 | semidirect |
| 20. C2×C4⋊Dic251 | C22 | 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 |
| 31. C22⋊(C251⋊C8) | C22 | semidirect |
| 32. C22⋊(C251⋊C8) | C22 | semidirect |
| 134. C251 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632170 | 2 |
| #30632008 | 2 |
| #30632003 | 2 |
| #30631998 | 2 |
| #30631730 | 2 |
| #30631723 | 2 |
| #30631692 | 2 |
| C2×#22548636 | 2 |
| #30631654 | 2 |
| #535×C251 | 2 |
| #3096 | 251 |