Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #30632340 | C2 | semidirect |
| 2. #30632322 | C2 | semidirect |
| 3. #30631999 | C2 | semidirect |
| 4. #30631964 | C2 | semidirect |
| 5. #30631922 | C2 | semidirect |
| 6. #30631879 | C2 | semidirect |
| 7. #30631822 | C2 | semidirect |
| 8. C4×D2008 | C2 | semidirect |
| 9. C8×D1004 | C2 | semidirect |
| 10. #102×D251 | C2 | semidirect |
| 11. #486×C251 | C2 | semidirect |
| 16. C2×#16860795 | C22 | semidirect |
| 17. C2×C8×D251 | C22 | semidirect |
| 20. #22548690 | C22 | semidirect |
| 26. C4×D1004 | C22 | semidirect |
| 27. C4⋊C4×D251 | C22 | semidirect |
| 28. #22548649 | C22 | semidirect |
| 29. #22548648 | C22 | semidirect |
| 30. C4⋊(C251⋊C8) | C22 | semidirect |
| 32. #22548637 | C22 | semidirect |
| 33. #22548636 | C22 | semidirect |
| 35. (C2×D251)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C251 | C22 | semidirect |
| 38. #102×C251 | C22 | semidirect |
| 39. #102×C251 | C22 | semidirect |
| 40. C4×C8×C251 | C22 | semidirect |
| 88. D1004 | D8 | semidirect |
| 89. D1004 | #41 | semidirect |
| 142. C251 | #3294 | semidirect |
| 146. #486 | D251 | semidirect |
| 161. C4⋊Q8 | C2×D251 | semidirect |
| 180. #102 | C2×D251 | semidirect |
| 181. #102 | C2×D251 | semidirect |
| 183. C4×C8 | C2×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632340 | 2 |
| #30632322 | 2 |
| #30631999 | 2 |
| #30631964 | 2 |
| #30631922 | 2 |
| #30631879 | 2 |
| #30631822 | 2 |
| C4×D2008 | 2 |
| C8×D1004 | 2 |
| #102×D251 | 2 |
| #486×C251 | 2 |
| #3294 | 251 |