Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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. #30631704 | C2 | semidirect |
| 3. #30631697 | C2 | semidirect |
| 4. #30631695 | C2 | semidirect |
| 5. #30631669 | C2 | semidirect |
| 6. #30631660 | C2 | semidirect |
| 7. #421×C251 | C2 | semidirect |
| 15. C2×#16860809 | C4 | semidirect |
| 18. C2×Q8×D251 | C4 | semidirect |
| 146. C251 | #1796 | semidirect |
| 150. #421 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548762 | 2 |
| #30631704 | 2 |
| #30631697 | 2 |
| #30631695 | 2 |
| #30631669 | 2 |
| #30631660 | 2 |
| #421×C251 | 2 |
| #1796 | 251 |