Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 2. #30631987 | C2 | semidirect |
| 3. #30631987 | C2 | semidirect |
| 4. #30631977 | C2 | semidirect |
| 5. #30631967 | C2 | semidirect |
| 6. #30631730 | C2 | semidirect |
| 7. #30631723 | C2 | semidirect |
| 8. #30631714 | C2 | semidirect |
| 14. #22548715 | C22 | semidirect |
| 16. #22548707 | 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 |
| 27. C4⋊(C251⋊C8) | C22 | semidirect |
| 28. C4⋊(C251⋊C8) | C22 | semidirect |
| 60. C2×D4×C251 | Q8 | semidirect |
| 124. C251 | #3081 | semidirect |
| 170. C2×D4 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632315 | 2 |
| #30631987 | 2 |
| #30631977 | 2 |
| #30631967 | 2 |
| #30631730 | 2 |
| #30631723 | 2 |
| #30631714 | 2 |
| #30631692 | 2 |
| C2×#22548636 | 2 |
| #518×C251 | 2 |
| #3081 | 251 |