Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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. C4⋊Q8×D251 | C2 | semidirect |
| 3. #30631983 | C2 | semidirect |
| 4. #30631979 | C2 | semidirect |
| 5. #30631977 | C2 | semidirect |
| 6. #30631971 | C2 | semidirect |
| 7. #30631965 | C2 | semidirect |
| 8. #30631726 | C2 | semidirect |
| 9. #30631709 | C2 | semidirect |
| 11. #476×C251 | C2 | semidirect |
| 44. #16860809 | Q8 | semidirect |
| 86. Dic502 | C2×Q8 | semidirect |
| 105. D4×C251 | C2×Q8 | semidirect |
| 137. C251 | #3079 | semidirect |
| 144. #476 | D251 | semidirect |
| 229. D4 | Q8×D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D251 | 2 |
| C4×#16860809 | 2 |
| #30631983 | 2 |
| #30631979 | 2 |
| #30631977 | 2 |
| #30631971 | 2 |
| #30631965 | 2 |
| #30631726 | 2 |
| #30631709 | 2 |
| #30631685 | 2 |
| #476×C251 | 2 |
| #3079 | 251 |