Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4×D1004 | C2 | semidirect |
| 2. #30631998 | C2 | semidirect |
| 3. #30631964 | C2 | semidirect |
| 4. #30631879 | C2 | semidirect |
| 5. #30631820 | C2 | semidirect |
| 6. C4×#16860795 | C2 | semidirect |
| 7. #30631740 | C2 | semidirect |
| 8. #532×C251 | C2 | semidirect |
| 18. #22548648 | C22 | semidirect |
| 19. C4⋊(C251⋊C8) | C22 | semidirect |
| 20. #22548636 | C22 | semidirect |
| 23. C4×C251⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C251 | C22 | semidirect |
| 26. #127×C251 | C22 | semidirect |
| 31. C4×D4×C251 | C22 | semidirect |
| 71. D1004 | #41 | semidirect |
| 88. C2×C4×C251 | D8 | semidirect |
| 120. C251 | #3100 | semidirect |
| 122. #532 | D251 | semidirect |
| 134. C4⋊Q8 | C2×D251 | semidirect |
| 135. #127 | C2×D251 | semidirect |
| 144. C4×D4 | C2×D251 | semidirect |
| 208. C2×C4 | #16860795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1004 | 2 |
| #30631998 | 2 |
| #30631964 | 2 |
| #30631879 | 2 |
| #30631820 | 2 |
| C4×#16860795 | 2 |
| #30631740 | 2 |
| #532×C251 | 2 |
| #3100 | 251 |