Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
402 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 221 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. Q8×C251⋊C8 | C2 | semidirect |
| 2. #30631765 | C2 | semidirect |
| 3. #30631744 | C2 | semidirect |
| 4. C4×#16860794 | C2 | semidirect |
| 36. C251⋊C8 | #41 | semidirect |
| 38. Q8×C251 | M16 | semidirect |
| 63. C251 | #2971 | semidirect |
| 100. Q8 | #16860794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C251⋊C8 | 2 |
| #30631765 | 2 |
| #30631744 | 2 |
| C4×#16860794 | 2 |
| C4×#41×C251 | 2 |
| #2971 | 251 |