Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #30632235 | C2 | semidirect |
| 2. #30632222 | C2 | semidirect |
| 3. #30632097 | C2 | semidirect |
| 4. #30632074 | C2 | semidirect |
| 5. #30632047 | C2 | semidirect |
| 6. #30631939 | C2 | semidirect |
| 7. #30631932 | C2 | semidirect |
| 8. #30631778 | C2 | semidirect |
| 9. #30631767 | C2 | semidirect |
| 10. #30631639 | C2 | semidirect |
| 11. #490×C251 | C2 | semidirect |
| 99. C251⋊C8 | #41 | semidirect |
| 137. C251 | #3171 | semidirect |
| 143. #490 | D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632235 | 2 |
| #30632222 | 2 |
| #30632097 | 2 |
| #30632074 | 2 |
| #30632047 | 2 |
| #30631939 | 2 |
| #30631932 | 2 |
| #30631778 | 2 |
| #30631767 | 2 |
| #30631639 | 2 |
| #490×C251 | 2 |
| #3171 | 251 |