Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 1. D4×D1004 | C2 | semidirect |
| 2. #30632064 | C2 | semidirect |
| 3. #30631883 | C2 | semidirect |
| 4. #30631882 | C2 | semidirect |
| 5. #30631430 | C2 | semidirect |
| 6. #30631416 | C2 | semidirect |
| 7. D4⋊C8×C251 | C2 | semidirect |
| 14. #22548712 | C22 | semidirect |
| 19. C4⋊(C251⋊C8) | C22 | semidirect |
| 23. C4⋊C8×C251 | C22 | semidirect |
| 24. C4×C8×C251 | C22 | semidirect |
| 72. D1004 | D8 | semidirect |
| 80. D4×C251 | D8 | semidirect |
| 117. C251 | #1619 | semidirect |
| 125. D4⋊C8 | D251 | semidirect |
| 139. C4⋊C8 | C2×D251 | semidirect |
| 142. C4×C8 | C2×D251 | semidirect |
| 194. D4 | D2008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D1004 | 2 |
| #30632064 | 2 |
| #30631883 | 2 |
| #30631882 | 2 |
| #30631430 | 2 |
| #30631416 | 2 |
| D4⋊C8×C251 | 2 |
| #1619 | 251 |