Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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. #30631739 | C2 | semidirect |
| 3. C4×C8×D251 | C2 | semidirect |
| 4. Q8⋊(C251⋊C8) | C2 | semidirect |
| 5. #30631416 | C2 | semidirect |
| 6. #30631414 | C2 | semidirect |
| 7. Q8⋊C8×C251 | C2 | semidirect |
| 28. #16860811 | C8 | semidirect |
| 61. D1004 | C2×C8 | semidirect |
| 78. Q8×C251 | C2×C8 | semidirect |
| 109. C251 | #1476 | semidirect |
| 115. Q8⋊C8 | D251 | semidirect |
| 170. Q8 | C8×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16860811 | 2 |
| #30631739 | 2 |
| C4×C8×D251 | 2 |
| Q8⋊(C251⋊C8) | 2 |
| #30631416 | 2 |
| #30631414 | 2 |
| Q8⋊C8×C251 | 2 |
| #1476 | 251 |