Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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. #30631738 | C2 | semidirect |
| 3. #30631709 | C2 | semidirect |
| 4. #30631416 | C2 | semidirect |
| 5. D4⋊(C251⋊C8) | C2 | semidirect |
| 6. #30631414 | C2 | semidirect |
| 7. D4⋊C8×C251 | C2 | semidirect |
| 19. C4⋊(C251⋊C8) | C22 | semidirect |
| 23. C4×C251⋊C8 | C22 | semidirect |
| 25. C4⋊C8×C251 | C22 | semidirect |
| 26. C4×C8×C251 | C22 | semidirect |
| 65. D1004 | M16 | semidirect |
| 85. D4×C251 | M16 | semidirect |
| 121. C251 | #1486 | semidirect |
| 129. D4⋊C8 | D251 | semidirect |
| 145. C4⋊C8 | C2×D251 | semidirect |
| 148. C4×C8 | C2×D251 | semidirect |
| 191. D4 | #16860793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×D251 | 2 |
| #30631738 | 2 |
| #30631709 | 2 |
| #30631416 | 2 |
| D4⋊(C251⋊C8) | 2 |
| #30631414 | 2 |
| D4⋊C8×C251 | 2 |
| #1486 | 251 |