Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 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. C22×C4⋊Dic127 | C2 | semidirect |
| 4. C22×Dic127⋊C4 | C2 | semidirect |
| 5. C2×C4⋊C4×D127 | C2 | direct (N × H) |
| 6. C22×C4⋊C4×C127 | C2 | semidirect |
| 11. C22×C4×D127 | C4 | semidirect |
| 14. C2×C4⋊Dic127 | C22 | semidirect |
| 15. C2×Dic127⋊C4 | C22 | semidirect |
| 16. C4⋊C4×D127 | C22 | direct (N × H) |
| 19. C2×C4⋊C4×C127 | C22 | semidirect |
| 25. C22×Dic127 | C2×C4 | semidirect |
| 29. C2×C4×D127 | C2×C4 | semidirect |
| 32. C4⋊Dic127 | C23 | semidirect |
| 33. Dic127⋊C4 | C23 | semidirect |
| 36. C22×C4×C127 | C2×C4 | semidirect |
| 39. C4⋊C4×C127 | C23 | semidirect |
| 40. C22×D127 | C4⋊C4 | direct (N × H) |
| 46. C2×Dic127 | C22×C4 | semidirect |
| 50. C4×D127 | C22×C4 | semidirect |
| 56. C2×C4×C127 | C22×C4 | semidirect |
| 59. C22×C127 | C2×C4⋊C4 | semidirect |
| 64. C2×D127 | C2×C4⋊C4 | direct (N × H) |
| 69. C4×C127 | C23×C4 | semidirect |
| 71. Dic127 | C23×C4 | semidirect |
| 72. C2×C127 | C22×C4⋊C4 | semidirect |
| 76. D127 | C22×C4⋊C4 | direct (N × H) |
| 78. C127 | C23×C4⋊C4 | semidirect |
| 84. C22×C4⋊C4 | D127 | direct (N × H) |
| 97. C2×C4⋊C4 | C2×D127 | direct (N × H) |
| 112. C22×C4 | C4×D127 | semidirect |
| 117. C4⋊C4 | C22×D127 | direct (N × H) |
| 134. C2×C4 | C2×C4×D127 | semidirect |
| 141. C22 | C4⋊C4×D127 | direct (N × H) |
| 149. C4 | C22×C4×D127 | semidirect |
| 151. C2 | C2×C4⋊C4×D127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D127 | 2 |
| C22×C4⋊Dic127 | 2 |
| C22×Dic127⋊C4 | 2 |
| C2×C4⋊C4×D127 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C23×C4⋊C4 | 127 |