Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 205 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. C2×C4×D1004 | C2 | semidirect |
| 3. #30631797 | C2 | direct (N × H) |
| 4. C2×#22548646 | C2 | semidirect |
| 5. C2×#22548636 | C2 | semidirect |
| 6. C2×#22548635 | C2 | semidirect |
| 7. C2×#22548626 | C2 | semidirect |
| 8. C2×C4×D4×C251 | C2 | semidirect |
| 11. C2×#16860795 | C4 | semidirect |
| 16. C4×D1004 | C22 | semidirect |
| 19. #22548646 | C22 | semidirect |
| 20. #22548636 | C22 | semidirect |
| 21. #22548635 | C22 | semidirect |
| 22. #22548626 | C22 | semidirect |
| 26. C4×D4×C251 | C22 | semidirect |
| 33. C2×D1004 | C2×C4 | semidirect |
| 38. #16860795 | C2×C4 | semidirect |
| 40. C2×C251⋊C8 | C2×C4 | semidirect |
| 49. C2×D4×C251 | C2×C4 | semidirect |
| 68. D1004 | C22×C4 | semidirect |
| 73. C251⋊C8 | C22×C4 | semidirect |
| 81. D4×C251 | C22×C4 | semidirect |
| 113. C2×C251 | #442 | semidirect |
| 118. C251 | C2×#442 | semidirect |
| 122. C2×C4×D4 | D251 | semidirect |
| 139. C4×D4 | C2×D251 | semidirect |
| 157. C2×D4 | C4×D251 | semidirect |
| 195. D4 | C2×C4×D251 | semidirect |
| 233. C2 | #30631797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16860795 | 2 |
| C2×C4×D1004 | 2 |
| #30631797 | 2 |
| C2×#22548646 | 2 |
| C2×#22548636 | 2 |
| C2×#22548635 | 2 |
| C2×#22548626 | 2 |
| C2×C4×D4×C251 | 2 |
| C2×#442 | 251 |