Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 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. C2×#22548741 | C2 | semidirect |
| 2. #30632237 | C2 | semidirect |
| 3. #30631902 | C2 | semidirect |
| 4. #30631892 | C2 | semidirect |
| 5. #30631882 | C2 | semidirect |
| 6. #30631711 | C2 | semidirect |
| 7. #30631686 | C2 | semidirect |
| 8. C2×C4×D4×C251 | C2 | semidirect |
| 14. #22548715 | C22 | semidirect |
| 15. #22548712 | C22 | semidirect |
| 16. #22548703 | C22 | semidirect |
| 21. C4⋊(C251⋊C8) | C22 | semidirect |
| 22. C4⋊(C251⋊C8) | C22 | semidirect |
| 23. #22548638 | C22 | semidirect |
| 24. #22548635 | C22 | semidirect |
| 53. C2×D4×C251 | D4 | semidirect |
| 119. C4×C251 | AGL(1,ℤ/8) | semidirect |
| 129. C251 | #3036 | semidirect |
| 133. C2×C4×D4 | D251 | semidirect |
| 174. C2×D4 | D1004 | semidirect |
| 250. C4 | #22548741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548741 | 2 |
| #30632237 | 2 |
| #30631902 | 2 |
| #30631892 | 2 |
| #30631882 | 2 |
| #30631711 | 2 |
| #30631686 | 2 |
| C2×C4×D4×C251 | 2 |
| #3036 | 251 |