Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 440 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. C2×D8×D127 | C2 | semidirect |
| 2. C2×D2032 | C2 | semidirect |
| 3. C2×#16861150 | C2 | semidirect |
| 4. D16×D127 | C2 | direct (N × H) |
| 5. C2×C16×D127 | C2 | semidirect |
| 6. C2×D16×C127 | C2 | semidirect |
| 8. C2×D1016 | C22 | semidirect |
| 11. D8×D127 | C22 | semidirect |
| 13. D2032 | C22 | semidirect |
| 14. #16861150 | C22 | semidirect |
| 15. C2×C127⋊C16 | C22 | semidirect |
| 16. C16×D127 | C22 | semidirect |
| 17. C2×D8×C127 | C22 | semidirect |
| 18. D16×C127 | C22 | semidirect |
| 19. C2×C16×C127 | C22 | semidirect |
| 27. D1016 | C23 | semidirect |
| 32. C127⋊C16 | C23 | semidirect |
| 35. D8×C127 | C23 | semidirect |
| 37. C16×C127 | C23 | semidirect |
| 61. C2×D127 | D16 | direct (N × H) |
| 67. C2×C127 | C2×D16 | semidirect |
| 70. D127 | C2×D16 | direct (N × H) |
| 72. C127 | C22×D16 | semidirect |
| 77. C2×D16 | D127 | direct (N × H) |
| 84. C2×D8 | C2×D127 | semidirect |
| 88. D16 | C2×D127 | direct (N × H) |
| 91. C2×C16 | C2×D127 | semidirect |
| 103. D8 | C22×D127 | semidirect |
| 109. C16 | C22×D127 | semidirect |
| 141. C2 | D16×D127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D127 | 2 |
| C2×D2032 | 2 |
| C2×#16861150 | 2 |
| D16×D127 | 2 |
| C2×C16×D127 | 2 |
| C2×D16×C127 | 2 |
| C22×D16 | 127 |