Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22550279 | C2 | semidirect |
| 4. #22550210 | C2 | semidirect |
| 5. #22550202 | C2 | semidirect |
| 6. #22550157 | C2 | semidirect |
| 7. #22550125 | C2 | semidirect |
| 8. C4×#14523235 | C2 | semidirect |
| 9. #22549953 | C2 | semidirect |
| 10. #22549915 | C2 | semidirect |
| 11. #475×C127 | C2 | semidirect |
| 89. C127⋊C8 | #41 | semidirect |
| 123. C127 | #3353 | semidirect |
| 129. #475 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550599 | 2 |
| #22550529 | 2 |
| #22550279 | 2 |
| #22550210 | 2 |
| #22550202 | 2 |
| #22550157 | 2 |
| #22550125 | 2 |
| C4×#14523235 | 2 |
| #22549953 | 2 |
| #22549915 | 2 |
| #475×C127 | 2 |
| #3353 | 127 |