Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4⋊Q8×D251 | C2 | semidirect |
| 3. #30632049 | C2 | semidirect |
| 4. #30632047 | C2 | semidirect |
| 5. #30632046 | C2 | semidirect |
| 6. #30632036 | C2 | semidirect |
| 7. #30632032 | C2 | semidirect |
| 8. #30631687 | C2 | semidirect |
| 9. #30631685 | C2 | semidirect |
| 10. #30631639 | C2 | semidirect |
| 11. #489×C251 | C2 | semidirect |
| 140. C251 | #3141 | semidirect |
| 147. #489 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632236 | 2 |
| C4⋊Q8×D251 | 2 |
| #30632049 | 2 |
| #30632047 | 2 |
| #30632046 | 2 |
| #30632036 | 2 |
| #30632032 | 2 |
| #30631687 | 2 |
| #30631685 | 2 |
| #30631639 | 2 |
| #489×C251 | 2 |
| #3141 | 251 |