Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 183 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. Q8×C251⋊C8 | C2 | semidirect |
| 3. #30631766 | C2 | semidirect |
| 4. #30631764 | C2 | semidirect |
| 5. #30631743 | C2 | semidirect |
| 6. C4×#16860793 | C2 | semidirect |
| 7. C8×Q8×C251 | C2 | semidirect |
| 53. C251⋊C8 | #41 | semidirect |
| 54. Q8×C251 | M16 | semidirect |
| 59. C8×C251 | #41 | semidirect |
| 75. C251 | #2971 | semidirect |
| 79. C8×Q8 | D251 | semidirect |
| 120. Q8 | #16860793 | semidirect |
| 135. C8 | #16860811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16860811 | 2 |
| Q8×C251⋊C8 | 2 |
| #30631766 | 2 |
| #30631764 | 2 |
| #30631743 | 2 |
| C4×#16860793 | 2 |
| C8×Q8×C251 | 2 |
| #2971 | 251 |