Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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. #22550350 | C2 | semidirect |
| 3. #22549989 | C2 | semidirect |
| 4. C4×D1016 | C2 | semidirect |
| 5. #22549914 | C2 | semidirect |
| 6. #22549882 | C2 | semidirect |
| 7. #405×C127 | C2 | semidirect |
| 9. C2×D1016 | C4 | semidirect |
| 12. C4×D508 | C22 | semidirect |
| 16. #16861143 | C22 | semidirect |
| 17. #16861141 | C22 | semidirect |
| 18. #16861131 | C22 | semidirect |
| 22. #97×C127 | C22 | semidirect |
| 23. C4×C8×C127 | C22 | semidirect |
| 27. C2×D508 | C2×C4 | semidirect |
| 30. D1016 | C2×C4 | semidirect |
| 31. D1016 | C2×C4 | semidirect |
| 38. C2×C8×C127 | C2×C4 | semidirect |
| 78. C127 | #2948 | semidirect |
| 85. #405 | D127 | semidirect |
| 100. #97 | C2×D127 | semidirect |
| 101. C4×C8 | C2×D127 | semidirect |
| 112. C2×C8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1016 | 2 |
| #22550350 | 2 |
| #22549989 | 2 |
| C4×D1016 | 2 |
| #22549914 | 2 |
| #22549882 | 2 |
| #405×C127 | 2 |
| #2948 | 127 |