Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 3. #22549974 | C2 | semidirect |
| 4. C4×#14523235 | C2 | semidirect |
| 5. #22549912 | C2 | semidirect |
| 6. #22549885 | C2 | semidirect |
| 8. #22549832 | C2 | semidirect |
| 9. #519×C127 | C2 | semidirect |
| 11. C2×#14523235 | C4 | semidirect |
| 20. #16861142 | C22 | semidirect |
| 21. #16861140 | C22 | semidirect |
| 22. #16861133 | C22 | semidirect |
| 24. #16861120 | C22 | semidirect |
| 25. C4×C127⋊C8 | C22 | semidirect |
| 28. C4×Q8×C127 | C22 | semidirect |
| 38. #14523235 | C2×C4 | semidirect |
| 39. #14523235 | C2×C4 | semidirect |
| 41. C2×C127⋊C8 | C2×C4 | semidirect |
| 51. C2×Q8×C127 | C2×C4 | semidirect |
| 104. C127 | #2949 | semidirect |
| 106. #519 | D127 | semidirect |
| 122. C4×Q8 | C2×D127 | semidirect |
| 139. C2×Q8 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523235 | 2 |
| #22550350 | 2 |
| #22549974 | 2 |
| C4×#14523235 | 2 |
| #22549912 | 2 |
| #22549885 | 2 |
| #22549880 | 2 |
| #22549832 | 2 |
| #519×C127 | 2 |
| #2949 | 127 |