Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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. #30632237 | C2 | semidirect |
| 2. #30632005 | C2 | semidirect |
| 3. #30631977 | C2 | semidirect |
| 4. #30631882 | C2 | semidirect |
| 5. #30631821 | C2 | semidirect |
| 6. #30631797 | C2 | semidirect |
| 7. #30631744 | C2 | semidirect |
| 8. C2×C4×D4×C251 | C2 | semidirect |
| 11. #22548715 | C22 | semidirect |
| 12. #22548712 | C22 | semidirect |
| 17. C4×D1004 | C22 | semidirect |
| 18. #22548646 | C22 | semidirect |
| 19. C4⋊(C251⋊C8) | C22 | semidirect |
| 21. #22548635 | C22 | semidirect |
| 23. #22548626 | C22 | semidirect |
| 81. D4×C251 | #41 | semidirect |
| 120. C251 | #3109 | semidirect |
| 123. C2×C4×D4 | D251 | semidirect |
| 199. D4 | #16860810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632237 | 2 |
| #30632005 | 2 |
| #30631977 | 2 |
| #30631882 | 2 |
| #30631821 | 2 |
| #30631797 | 2 |
| #30631744 | 2 |
| C2×C4×D4×C251 | 2 |
| #3109 | 251 |