Finite Group DatabasebetaFinite Group DatabasebetaOrder 32128.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#22548643 | C2 | semidirect |
| 3. C2×#22548642 | C2 | semidirect |
| 4. C2×#22548641 | C2 | semidirect |
| 5. M16×Dic251 | C2 | semidirect |
| 6. C4×Dic251⋊C4 | C2 | semidirect |
| 7. C2×#104×C251 | C2 | semidirect |
| 10. #22548713 | C4 | semidirect |
| 11. #22548711 | C4 | semidirect |
| 12. #22548704 | C4 | semidirect |
| 13. #22548702 | C4 | semidirect |
| 45. #16860794 | D4 | semidirect |
| 71. M16×C251 | D4 | semidirect |
| 140. Dic251 | #104 | semidirect |
| 148. C251 | #1980 | semidirect |
| 154. C2×#104 | D251 | semidirect |
| 206. M16 | C22⋊D251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632233 | 2 |
| C2×#22548643 | 2 |
| C2×#22548642 | 2 |
| C2×#22548641 | 2 |
| M16×Dic251 | 2 |
| C4×Dic251⋊C4 | 2 |
| C2×#104×C251 | 2 |
| #1980 | 251 |