Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 4. #30631419 | C2 | semidirect |
| 5. Q8⋊(C251⋊C8) | C2 | semidirect |
| 6. #30631417 | C2 | semidirect |
| 7. Q8⋊C8×C251 | C2 | semidirect |
| 60. Dic502 | M16 | semidirect |
| 76. Q8×C251 | M16 | semidirect |
| 104. C251 | #1487 | semidirect |
| 112. Q8⋊C8 | D251 | semidirect |
| 167. Q8 | #16860793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D251 | 2 |
| #30631738 | 2 |
| #30631709 | 2 |
| #30631419 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| #30631417 | 2 |
| Q8⋊C8×C251 | 2 |
| #1487 | 251 |