Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22548740 | C2 | semidirect |
| 2. C2×C4×D1004 | C2 | semidirect |
| 3. #30631899 | C2 | semidirect |
| 4. #30631889 | C2 | semidirect |
| 5. #30631879 | C2 | semidirect |
| 6. #30631711 | C2 | semidirect |
| 7. #30631688 | C2 | semidirect |
| 8. #532×C251 | C2 | semidirect |
| 21. C4⋊(C251⋊C8) | C22 | semidirect |
| 22. C4⋊(C251⋊C8) | C22 | semidirect |
| 23. #22548639 | C22 | semidirect |
| 24. #22548636 | C22 | semidirect |
| 26. C4⋊Q8×C251 | C22 | semidirect |
| 27. #127×C251 | C22 | semidirect |
| 28. #124×C251 | C22 | semidirect |
| 37. C2×D1004 | D4 | semidirect |
| 119. C4×C251 | AGL(1,ℤ/8) | semidirect |
| 129. C251 | #3036 | semidirect |
| 132. #532 | D251 | semidirect |
| 146. C4⋊Q8 | C2×D251 | semidirect |
| 147. #127 | C2×D251 | semidirect |
| 148. #124 | C2×D251 | semidirect |
| 250. C4 | #22548740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548740 | 2 |
| C2×C4×D1004 | 2 |
| #30631899 | 2 |
| #30631889 | 2 |
| #30631879 | 2 |
| #30631711 | 2 |
| #30631688 | 2 |
| #532×C251 | 2 |
| #3036 | 251 |