Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 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 |
|---|---|---|
| 2. #30631984 | C2 | semidirect |
| 3. #30631974 | C2 | semidirect |
| 4. #30631964 | C2 | semidirect |
| 5. #30631730 | C2 | semidirect |
| 6. #30631711 | C2 | semidirect |
| 8. #533×C251 | C2 | semidirect |
| 18. #22548648 | C22 | semidirect |
| 19. #22548646 | C22 | semidirect |
| 20. C4⋊(C251⋊C8) | C22 | semidirect |
| 21. C4⋊(C251⋊C8) | C22 | semidirect |
| 24. C4⋊Q8×C251 | C22 | semidirect |
| 25. C4⋊Q8×C251 | C22 | semidirect |
| 26. #125×C251 | C22 | semidirect |
| 36. C2×D1004 | Q8 | semidirect |
| 115. C251 | #3077 | semidirect |
| 117. #533 | D251 | semidirect |
| 128. C4⋊Q8 | C2×D251 | semidirect |
| 129. C4⋊Q8 | C2×D251 | semidirect |
| 130. #125 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1004 | 2 |
| #30631984 | 2 |
| #30631974 | 2 |
| #30631964 | 2 |
| #30631730 | 2 |
| #30631711 | 2 |
| #30631691 | 2 |
| #533×C251 | 2 |
| #3077 | 251 |