Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C2×#22548713 | C2 | semidirect |
| 5. #30631891 | C2 | direct (N × H) |
| 6. C2×Dic251⋊C8 | C2 | semidirect |
| 7. C2×#22548638 | C2 | semidirect |
| 8. C2×#103×C251 | C2 | semidirect |
| 18. #22548713 | C22 | semidirect |
| 25. Dic251⋊C8 | C22 | semidirect |
| 26. #22548638 | C22 | semidirect |
| 30. #103×C251 | C22 | semidirect |
| 78. C2×Dic251 | SD16 | semidirect |
| 111. Dic251 | C2×SD16 | semidirect |
| 112. C2×C251 | #461 | semidirect |
| 117. C251 | C2×#461 | semidirect |
| 126. C2×#103 | D251 | semidirect |
| 148. #103 | C2×D251 | semidirect |
| 231. C2 | #30631891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860799 | 2 |
| C22×#16860797 | 2 |
| C2×#22548713 | 2 |
| C2×#22548677 | 2 |
| #30631891 | 2 |
| C2×Dic251⋊C8 | 2 |
| C2×#22548638 | 2 |
| C2×#103×C251 | 2 |
| C2×#461 | 251 |