Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22548745 | C2 | semidirect |
| 2. C2×#22548702 | C2 | semidirect |
| 3. #41×Dic251 | C2 | semidirect |
| 4. #30631907 | C2 | semidirect |
| 5. #30631900 | C2 | semidirect |
| 6. #30631710 | C2 | semidirect |
| 7. #30631697 | C2 | semidirect |
| 8. #30631692 | C2 | semidirect |
| 12. C2×#16860800 | C22 | semidirect |
| 13. C2×#16860798 | C22 | semidirect |
| 18. Q8×Dic251 | C22 | semidirect |
| 20. D4×Dic251 | C22 | semidirect |
| 26. Dic251⋊C8 | C22 | semidirect |
| 27. #22548640 | C22 | semidirect |
| 125. C251 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548745 | 2 |
| C2×#22548702 | 2 |
| #41×Dic251 | 2 |
| #30631907 | 2 |
| #30631900 | 2 |
| #30631710 | 2 |
| #30631697 | 2 |
| #30631692 | 2 |
| C2×AGL(1,ℤ/8)×C251 | 2 |
| #3040 | 251 |