Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
2528 conjugacy classes of subgroups; only the 1197 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 1197 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. C24×Dic127 | C2 | semidirect |
| 2. C2×D4×Dic127 | C2 | direct (N × H) |
| 3. C22×C4⋊Dic127 | C2 | semidirect |
| 4. C22×C22⋊Dic127 | C2 | semidirect |
| 5. C22×C4×Dic127 | C2 | semidirect |
| 11. C23×Dic127 | C22 | semidirect |
| 12. D4×Dic127 | C22 | direct (N × H) |
| 13. C2×C4⋊Dic127 | C22 | semidirect |
| 14. C2×C22⋊Dic127 | C22 | semidirect |
| 15. C2×C4×Dic127 | C22 | semidirect |
| 17. C22×D4×C127 | C4 | semidirect |
| 23. C22×Dic127 | D4 | direct (N × H) |
| 27. C22×Dic127 | C23 | semidirect |
| 28. C4⋊Dic127 | C23 | semidirect |
| 29. C22⋊Dic127 | C23 | semidirect |
| 30. C4×Dic127 | C23 | semidirect |
| 33. C24×C127 | C2×C4 | semidirect |
| 36. C2×D4×C127 | C2×C4 | semidirect |
| 38. C22×C4×C127 | C2×C4 | semidirect |
| 43. C2×Dic127 | C2×D4 | direct (N × H) |
| 51. C23×C127 | C22×C4 | semidirect |
| 56. D4×C127 | C22×C4 | semidirect |
| 57. C2×C4×C127 | C22×C4 | semidirect |
| 62. C22×C127 | C4×D4 | semidirect |
| 64. C22×C127 | C23×C4 | semidirect |
| 68. C4×C127 | C23×C4 | semidirect |
| 71. Dic127 | C22×D4 | direct (N × H) |
| 73. C2×C127 | C2×C4×D4 | semidirect |
| 78. C127 | C22×C4×D4 | semidirect |
| 86. C22×D4 | Dic127 | direct (N × H) |
| 100. C24 | C2×Dic127 | semidirect |
| 103. C2×D4 | C2×Dic127 | direct (N × H) |
| 113. C22×C4 | C2×Dic127 | semidirect |
| 122. C23 | C22×Dic127 | semidirect |
| 127. D4 | C22×Dic127 | direct (N × H) |
| 135. C2×C4 | C22×Dic127 | semidirect |
| 140. C22 | D4×Dic127 | direct (N × H) |
| 142. C22 | C23×Dic127 | semidirect |
| 149. C4 | C23×Dic127 | semidirect |
| 151. C2 | C2×D4×Dic127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic127 | 2 |
| C2×D4×Dic127 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×C22⋊Dic127 | 2 |
| C22×C4×Dic127 | 2 |
| C23×D4×C127 | 2 |
| C22×C4×D4 | 127 |