Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
4632 conjugacy classes of subgroups; only the 1413 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1413 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. C24×Dic127 | C2 | semidirect |
| 3. C22×(C2×D127)⋊C4 | C2 | direct (N × H) |
| 4. C24×C4×C127 | C2 | semidirect |
| 7. C24×D127 | C4 | semidirect |
| 10. C23×Dic127 | C22 | semidirect |
| 11. C2×(C2×D127)⋊C4 | C22 | direct (N × H) |
| 14. C23×C4×C127 | C22 | semidirect |
| 18. C23×D127 | C2×C4 | semidirect |
| 21. C22×Dic127 | C23 | semidirect |
| 22. (C2×D127)⋊C4 | C23 | direct (N × H) |
| 28. C22×C4×C127 | C23 | semidirect |
| 32. C22×D127 | C22×C4 | semidirect |
| 35. C2×Dic127 | C24 | semidirect |
| 36. C23×C127 | C22⋊C4 | semidirect |
| 42. C2×C4×C127 | C24 | semidirect |
| 43. C22×C127 | C2×C22⋊C4 | semidirect |
| 51. C2×D127 | C23×C4 | semidirect |
| 54. C2×C127 | C22×C22⋊C4 | semidirect |
| 60. C127 | C23×C22⋊C4 | semidirect |
| 63. C24×C4 | D127 | semidirect |
| 73. C23×C4 | C2×D127 | semidirect |
| 87. C22×C4 | C22×D127 | semidirect |
| 94. C23 | (C2×D127)⋊C4 | direct (N × H) |
| 102. C2×C4 | C23×D127 | semidirect |
| 107. C22 | C2×(C2×D127)⋊C4 | direct (N × H) |
| 115. C2 | C22×(C2×D127)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×D127 | 2 |
| C24×Dic127 | 2 |
| C22×(C2×D127)⋊C4 | 2 |
| C24×C4×C127 | 2 |
| C23×C22⋊C4 | 127 |