Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22550356 | C2 | semidirect |
| 3. #22550216 | C2 | semidirect |
| 4. #22550210 | C2 | semidirect |
| 5. #22550198 | C2 | semidirect |
| 6. #22550188 | C2 | semidirect |
| 7. #22549919 | C2 | semidirect |
| 8. C2×#16861143 | C2 | semidirect |
| 9. #22549877 | C2 | semidirect |
| 10. #22549842 | C2 | semidirect |
| 11. #416×C127 | C2 | semidirect |
| 134. C127 | #3098 | semidirect |
| 144. #416 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550454 | 2 |
| #22550356 | 2 |
| #22550216 | 2 |
| #22550210 | 2 |
| #22550198 | 2 |
| #22550188 | 2 |
| #22549919 | 2 |
| C2×#16861143 | 2 |
| #22549877 | 2 |
| #22549842 | 2 |
| #416×C127 | 2 |
| #3098 | 127 |