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. #22550357 | C2 | semidirect |
| 3. #22550219 | C2 | semidirect |
| 4. #22550213 | C2 | semidirect |
| 5. #22550203 | C2 | semidirect |
| 6. #22550191 | C2 | semidirect |
| 7. #22549916 | C2 | semidirect |
| 8. #22549875 | C2 | semidirect |
| 9. #22549873 | C2 | semidirect |
| 10. #22549842 | C2 | semidirect |
| 11. C2×#107×C127 | C2 | semidirect |
| 134. C127 | #3098 | semidirect |
| 142. C2×#107 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550457 | 2 |
| #22550357 | 2 |
| #22550219 | 2 |
| #22550213 | 2 |
| #22550203 | 2 |
| #22550191 | 2 |
| #22549916 | 2 |
| #22549875 | 2 |
| #22549873 | 2 |
| #22549842 | 2 |
| C2×#107×C127 | 2 |
| #3098 | 127 |