Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 1. C22×#16860798 | C2 | semidirect |
| 2. #30632258 | C2 | semidirect |
| 3. #30632162 | C2 | semidirect |
| 4. #30631900 | C2 | semidirect |
| 5. #30631890 | C2 | semidirect |
| 6. #30631715 | C2 | semidirect |
| 7. #30631697 | C2 | semidirect |
| 8. #30631683 | C2 | semidirect |
| 14. #22548713 | C22 | semidirect |
| 15. #22548702 | C22 | semidirect |
| 23. Dic251⋊C8 | C22 | semidirect |
| 24. #22548640 | C22 | semidirect |
| 25. #22548639 | C22 | semidirect |
| 26. #22548636 | C22 | semidirect |
| 116. C251 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860798 | 2 |
| #30632258 | 2 |
| #30632162 | 2 |
| #30631900 | 2 |
| #30631890 | 2 |
| #30631715 | 2 |
| #30631697 | 2 |
| #30631683 | 2 |
| C2×AGL(1,ℤ/8)×C251 | 2 |
| #3042 | 251 |