Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #30632097 | C2 | semidirect |
| 4. #30632096 | C2 | semidirect |
| 5. #30632093 | C2 | semidirect |
| 6. #30632091 | C2 | semidirect |
| 7. #30632084 | C2 | semidirect |
| 11. #501×C251 | C2 | semidirect |
| 52. #16860793 | Q8 | semidirect |
| 95. C251⋊C8 | C2×Q8 | semidirect |
| 103. C8×C251 | C2×Q8 | semidirect |
| 124. C251 | #3165 | semidirect |
| 131. #501 | D251 | semidirect |
| 228. C8 | Q8×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632243 | 2 |
| C4⋊Q8×D251 | 2 |
| #30632097 | 2 |
| #30632096 | 2 |
| #30632093 | 2 |
| #30632091 | 2 |
| #30632084 | 2 |
| #30631728 | 2 |
| #30631726 | 2 |
| #30631639 | 2 |
| #501×C251 | 2 |
| #3165 | 251 |