Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. #22550429 | C2 | semidirect |
| 3. #22550243 | C2 | semidirect |
| 4. #22550239 | C2 | semidirect |
| 5. #22550237 | C2 | semidirect |
| 6. #22550234 | C2 | semidirect |
| 7. #22549873 | C2 | semidirect |
| 8. #22549872 | C2 | semidirect |
| 9. #22549870 | C2 | semidirect |
| 10. C2×#16861119 | C2 | semidirect |
| 11. #416×C127 | C2 | semidirect |
| 126. C127 | #3135 | semidirect |
| 136. #416 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550429 | 2 |
| #22550422 | 2 |
| #22550243 | 2 |
| #22550239 | 2 |
| #22550237 | 2 |
| #22550234 | 2 |
| #22549873 | 2 |
| #22549872 | 2 |
| #22549870 | 2 |
| C2×#16861119 | 2 |
| #416×C127 | 2 |
| #3135 | 127 |