Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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. #30632244 | C2 | semidirect |
| 2. #30631987 | C2 | semidirect |
| 3. #30631977 | C2 | semidirect |
| 4. #30631967 | C2 | semidirect |
| 5. #30631727 | C2 | semidirect |
| 6. #30631711 | C2 | semidirect |
| 10. #22548715 | C22 | semidirect |
| 11. #22548715 | C22 | semidirect |
| 12. #22548707 | C22 | semidirect |
| 18. #22548648 | C22 | semidirect |
| 19. #22548646 | C22 | semidirect |
| 20. C4⋊(C251⋊C8) | C22 | semidirect |
| 21. C4⋊(C251⋊C8) | C22 | semidirect |
| 48. C2×D4×C251 | Q8 | semidirect |
| 115. C251 | #3077 | semidirect |
| 154. C2×D4 | Dic502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632244 | 2 |
| #30631987 | 2 |
| #30631977 | 2 |
| #30631967 | 2 |
| #30631727 | 2 |
| #30631711 | 2 |
| #30631692 | 2 |
| C2×C4×D4×C251 | 2 |
| #3077 | 251 |