Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #30632232 | C2 | semidirect |
| 2. #30632091 | C2 | semidirect |
| 3. #30632062 | C2 | semidirect |
| 4. #30632032 | C2 | semidirect |
| 5. #30631923 | C2 | semidirect |
| 6. #30631921 | C2 | semidirect |
| 7. D8×Dic251 | C2 | semidirect |
| 8. #30631769 | C2 | semidirect |
| 9. #30631767 | C2 | semidirect |
| 10. C2×C8×Dic251 | C2 | semidirect |
| 11. #466×C251 | C2 | semidirect |
| 82. C2×Dic251 | D8 | semidirect |
| 89. C251⋊C8 | #41 | semidirect |
| 101. C8×C251 | #41 | semidirect |
| 127. C251 | #3169 | semidirect |
| 135. #466 | D251 | semidirect |
| 229. C8 | #16860809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632232 | 2 |
| #30632091 | 2 |
| #30632062 | 2 |
| #30632032 | 2 |
| #30631923 | 2 |
| #30631921 | 2 |
| D8×Dic251 | 2 |
| #30631769 | 2 |
| #30631767 | 2 |
| C2×C8×Dic251 | 2 |
| #466×C251 | 2 |
| #3169 | 251 |