Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 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. #30632242 | C2 | semidirect |
| 3. #30631986 | C2 | semidirect |
| 4. #30631985 | C2 | semidirect |
| 5. #30631974 | C2 | semidirect |
| 6. #30631968 | C2 | semidirect |
| 7. #30631967 | C2 | semidirect |
| 8. #30631726 | C2 | semidirect |
| 9. #30631709 | C2 | semidirect |
| 11. #476×C251 | C2 | semidirect |
| 15. #22548715 | C22 | semidirect |
| 16. #22548706 | C22 | semidirect |
| 30. #22548649 | C22 | semidirect |
| 31. #22548648 | C22 | semidirect |
| 32. #22548646 | C22 | semidirect |
| 33. C4⋊(C251⋊C8) | C22 | semidirect |
| 34. Dic251⋊C8 | C22 | semidirect |
| 38. C4⋊Q8×C251 | C22 | semidirect |
| 40. #106×C251 | C22 | semidirect |
| 41. C4⋊C8×C251 | C22 | semidirect |
| 48. D4×D251 | Q8 | semidirect |
| 144. C251 | #3077 | semidirect |
| 151. #476 | D251 | semidirect |
| 161. C4⋊Q8 | C2×D251 | semidirect |
| 180. #106 | 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 |
|---|---|
| #30632242 | 2 |
| C4×D4×D251 | 2 |
| #30631986 | 2 |
| #30631985 | 2 |
| #30631974 | 2 |
| #30631968 | 2 |
| #30631967 | 2 |
| #30631726 | 2 |
| #30631709 | 2 |
| #30631690 | 2 |
| #476×C251 | 2 |
| #3077 | 251 |