Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22548763 | C2 | semidirect |
| 2. C2×#22548735 | C2 | semidirect |
| 3. #30632265 | C2 | semidirect |
| 4. #30631848 | C2 | semidirect |
| 5. #30631841 | C2 | semidirect |
| 6. #30631831 | C2 | semidirect |
| 7. #30631824 | C2 | semidirect |
| 8. #30631689 | C2 | semidirect |
| 9. C2×#22548639 | C2 | semidirect |
| 10. #30631655 | C2 | semidirect |
| 11. C2×#137×C251 | C2 | semidirect |
| 52. #16860810 | D4 | semidirect |
| 86. C2×Q8×C251 | D4 | semidirect |
| 169. C251 | #3013 | semidirect |
| 172. C2×#137 | D251 | semidirect |
| 233. C2×Q8 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548763 | 2 |
| C2×#22548735 | 2 |
| #30632265 | 2 |
| #30631848 | 2 |
| #30631841 | 2 |
| #30631831 | 2 |
| #30631824 | 2 |
| #30631689 | 2 |
| C2×#22548639 | 2 |
| #30631655 | 2 |
| C2×#137×C251 | 2 |
| #3013 | 251 |