Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #22550642 | C2 | semidirect |
| 3. #22549999 | C2 | semidirect |
| 4. #22549994 | C2 | semidirect |
| 5. #22549925 | C2 | semidirect |
| 6. C2×#16861137 | C2 | semidirect |
| 7. C4×M16×C127 | C2 | semidirect |
| 9. #16861242 | C4 | semidirect |
| 10. #16861237 | C4 | semidirect |
| 13. #16861215 | C22 | semidirect |
| 16. #16861145 | C22 | semidirect |
| 17. #16861137 | C22 | semidirect |
| 18. #16861137 | C22 | semidirect |
| 22. #97×C127 | C22 | semidirect |
| 23. C4×C8×C127 | C22 | semidirect |
| 32. Dic508 | C2×C4 | semidirect |
| 33. #14523237 | C2×C4 | semidirect |
| 34. D1016 | C2×C4 | semidirect |
| 86. C127 | #2956 | semidirect |
| 93. C4×M16 | D127 | semidirect |
| 108. #97 | C2×D127 | semidirect |
| 109. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550676 | 2 |
| #22550642 | 2 |
| #22549999 | 2 |
| #22549994 | 2 |
| #22549925 | 2 |
| C2×#16861137 | 2 |
| C4×M16×C127 | 2 |
| #2956 | 127 |