Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. Q8×D508 | C2 | semidirect |
| 3. #22550228 | C2 | semidirect |
| 4. #22550208 | C2 | semidirect |
| 5. #22550106 | C2 | semidirect |
| 6. #22550082 | C2 | semidirect |
| 7. #22550016 | C2 | semidirect |
| 8. C4×#14523235 | C2 | semidirect |
| 9. #22549941 | C2 | semidirect |
| 10. #103×D127 | C2 | semidirect |
| 11. #475×C127 | C2 | semidirect |
| 85. D508 | SD16 | semidirect |
| 98. Q8×C127 | #41 | semidirect |
| 129. C127 | #3298 | semidirect |
| 134. #475 | D127 | semidirect |
| 213. Q8 | #14523249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D508 | 2 |
| #22550529 | 2 |
| #22550228 | 2 |
| #22550208 | 2 |
| #22550106 | 2 |
| #22550082 | 2 |
| #22550016 | 2 |
| C4×#14523235 | 2 |
| #22549941 | 2 |
| #103×D127 | 2 |
| #475×C127 | 2 |
| #3298 | 127 |