Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #30632035 | C2 | semidirect |
| 3. #30631889 | C2 | semidirect |
| 4. #30631430 | C2 | semidirect |
| 5. D4⋊(C251⋊C8) | C2 | semidirect |
| 6. #30631414 | C2 | semidirect |
| 7. #474×C251 | C2 | semidirect |
| 16. C4⋊(C251⋊C8) | C22 | semidirect |
| 19. C4×C251⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C251 | C22 | semidirect |
| 23. C4⋊C8×C251 | C22 | semidirect |
| 75. D4×C251 | SD16 | semidirect |
| 109. C251 | #1639 | semidirect |
| 113. #474 | D251 | semidirect |
| 121. C4⋊Q8 | C2×D251 | semidirect |
| 130. C4⋊C8 | C2×D251 | semidirect |
| 180. D4 | #16860797 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D1004 | 2 |
| #30632035 | 2 |
| #30631889 | 2 |
| #30631430 | 2 |
| D4⋊(C251⋊C8) | 2 |
| #30631414 | 2 |
| #474×C251 | 2 |
| #1639 | 251 |