Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #22550599 | C2 | semidirect |
| 3. #22550227 | C2 | semidirect |
| 4. #22550220 | C2 | semidirect |
| 5. #22550156 | C2 | semidirect |
| 6. #22550116 | C2 | semidirect |
| 7. #22550086 | C2 | semidirect |
| 8. #22550035 | C2 | semidirect |
| 9. C8×D508 | C2 | semidirect |
| 10. #22549869 | C2 | semidirect |
| 11. C4×SD16×C127 | C2 | semidirect |
| 126. C127 | #3302 | semidirect |
| 135. C4×SD16 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550599 | 2 |
| #22550530 | 2 |
| #22550227 | 2 |
| #22550220 | 2 |
| #22550156 | 2 |
| #22550116 | 2 |
| #22550086 | 2 |
| #22550035 | 2 |
| C8×D508 | 2 |
| #22549869 | 2 |
| C4×SD16×C127 | 2 |
| #3302 | 127 |