Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #30632039 | C2 | semidirect |
| 3. #30632028 | C2 | semidirect |
| 4. #30631964 | C2 | semidirect |
| 5. #30631926 | C2 | semidirect |
| 6. #30631897 | C2 | semidirect |
| 7. #30631847 | C2 | semidirect |
| 8. C4×#16860797 | C2 | semidirect |
| 9. D4×C251⋊C8 | C2 | semidirect |
| 10. #30631681 | C2 | semidirect |
| 11. #556×C251 | C2 | semidirect |
| 125. C251 | #3302 | semidirect |
| 127. #556 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632342 | 2 |
| #30632039 | 2 |
| #30632028 | 2 |
| #30631964 | 2 |
| #30631926 | 2 |
| #30631897 | 2 |
| #30631847 | 2 |
| C4×#16860797 | 2 |
| D4×C251⋊C8 | 2 |
| #30631681 | 2 |
| #556×C251 | 2 |
| #3302 | 251 |