Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22548742 | C2 | semidirect |
| 2. #30632238 | C2 | semidirect |
| 3. C4×D4×D251 | C2 | semidirect |
| 4. #30631905 | C2 | semidirect |
| 5. #30631904 | C2 | semidirect |
| 6. #30631889 | C2 | semidirect |
| 7. #30631883 | C2 | semidirect |
| 8. #30631882 | C2 | semidirect |
| 9. #30631709 | C2 | semidirect |
| 10. #30631687 | C2 | semidirect |
| 11. #461×C251 | C2 | semidirect |
| 20. #22548712 | C22 | semidirect |
| 21. #22548704 | C22 | semidirect |
| 34. C4⋊(C251⋊C8) | C22 | semidirect |
| 35. Dic251⋊C8 | C22 | semidirect |
| 36. #22548639 | C22 | semidirect |
| 37. #22548637 | C22 | semidirect |
| 38. #22548635 | C22 | semidirect |
| 40. C4⋊Q8×C251 | C22 | semidirect |
| 42. C4⋊C8×C251 | C22 | semidirect |
| 43. #103×C251 | C22 | semidirect |
| 54. D4×D251 | D4 | semidirect |
| 146. C4×C251 | AGL(1,ℤ/8) | semidirect |
| 160. C251 | #3036 | semidirect |
| 168. #461 | D251 | semidirect |
| 182. C4⋊Q8 | C2×D251 | semidirect |
| 200. C4⋊C8 | C2×D251 | semidirect |
| 202. #103 | C2×D251 | semidirect |
| 311. C4 | #22548742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548742 | 2 |
| #30632238 | 2 |
| C4×D4×D251 | 2 |
| #30631905 | 2 |
| #30631904 | 2 |
| #30631889 | 2 |
| #30631883 | 2 |
| #30631882 | 2 |
| #30631709 | 2 |
| #30631687 | 2 |
| #461×C251 | 2 |
| #3036 | 251 |