Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #22550274 | C2 | semidirect |
| 4. #22550215 | C2 | semidirect |
| 5. #22550205 | C2 | semidirect |
| 6. #22550171 | C2 | semidirect |
| 7. #22550161 | C2 | semidirect |
| 8. #22550131 | C2 | semidirect |
| 10. #22549917 | C2 | semidirect |
| 11. C4×Q16×C127 | C2 | semidirect |
| 117. C127 | #3356 | semidirect |
| 126. C4×Q16 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550599 | 2 |
| #22550586 | 2 |
| #22550274 | 2 |
| #22550215 | 2 |
| #22550205 | 2 |
| #22550171 | 2 |
| #22550161 | 2 |
| #22550131 | 2 |
| #22549955 | 2 |
| #22549917 | 2 |
| C4×Q16×C127 | 2 |
| #3356 | 127 |