Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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. C2×#22548740 | C2 | semidirect |
| 2. C22×D2008 | C2 | semidirect |
| 3. #30632251 | C2 | semidirect |
| 4. #30632073 | C2 | semidirect |
| 5. #30632072 | C2 | semidirect |
| 6. #30632062 | C2 | semidirect |
| 7. #30631642 | C2 | semidirect |
| 8. C2×#135×C251 | C2 | semidirect |
| 11. C2×#16860797 | C22 | semidirect |
| 15. C2×#16860795 | C22 | semidirect |
| 17. #22548711 | C22 | semidirect |
| 18. #22548704 | C22 | semidirect |
| 22. #22548625 | C22 | semidirect |
| 23. C8×Dic251 | C22 | semidirect |
| 26. C2×Q16×C251 | C22 | semidirect |
| 27. C2×SD16×C251 | C22 | semidirect |
| 28. C2×D8×C251 | C22 | semidirect |
| 40. #16860794 | D4 | semidirect |
| 56. C2×C8×C251 | D4 | semidirect |
| 101. C251 | #3155 | semidirect |
| 104. C2×#135 | D251 | semidirect |
| 115. C2×Q16 | C2×D251 | semidirect |
| 117. C2×SD16 | C2×D251 | semidirect |
| 122. C2×D8 | C2×D251 | semidirect |
| 154. C2×C8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| C22×D2008 | 2 |
| #30632251 | 2 |
| #30632073 | 2 |
| #30632072 | 2 |
| #30632062 | 2 |
| #30631642 | 2 |
| C2×#135×C251 | 2 |
| #3155 | 251 |