Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22548738 | C2 | semidirect |
| 2. #30632356 | C2 | semidirect |
| 3. #30632062 | C2 | semidirect |
| 4. #30631923 | C2 | semidirect |
| 5. #30631920 | C2 | semidirect |
| 6. #30631885 | C2 | semidirect |
| 7. #30631832 | C2 | semidirect |
| 8. #30631831 | C2 | semidirect |
| 9. Q16×Dic251 | C2 | semidirect |
| 10. C8×C22⋊D251 | C2 | semidirect |
| 11. C2×#135×C251 | C2 | semidirect |
| 74. Q16×C251 | D4 | semidirect |
| 134. Dic251 | #135 | semidirect |
| 142. C251 | #3287 | semidirect |
| 145. C2×#135 | D251 | semidirect |
| 202. Q16 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22548738 | 2 |
| #30632356 | 2 |
| #30632062 | 2 |
| #30631923 | 2 |
| #30631920 | 2 |
| #30631885 | 2 |
| #30631832 | 2 |
| #30631831 | 2 |
| Q16×Dic251 | 2 |
| C8×C22⋊D251 | 2 |
| C2×#135×C251 | 2 |
| #3287 | 251 |