Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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×Dic502 | C2 | semidirect |
| 3. #30632034 | C2 | semidirect |
| 4. #30632032 | C2 | semidirect |
| 5. #30631977 | C2 | semidirect |
| 6. #30631976 | C2 | semidirect |
| 7. #30631887 | C2 | semidirect |
| 8. #30631885 | C2 | semidirect |
| 9. C8×Dic502 | C2 | semidirect |
| 10. #30631772 | C2 | semidirect |
| 11. C4×SD16×C251 | C2 | semidirect |
| 77. Dic502 | SD16 | semidirect |
| 91. Q8×C251 | #41 | semidirect |
| 125. C251 | #3362 | semidirect |
| 137. C4×SD16 | D251 | semidirect |
| 206. Q8 | #16860810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic502 | 2 |
| #30632358 | 2 |
| #30632034 | 2 |
| #30632032 | 2 |
| #30631977 | 2 |
| #30631976 | 2 |
| #30631887 | 2 |
| #30631885 | 2 |
| C8×Dic502 | 2 |
| #30631772 | 2 |
| C4×SD16×C251 | 2 |
| #3362 | 251 |