Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 381 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. C2×C42×D127 | C2 | semidirect |
| 3. C4×Dic127⋊C4 | C2 | semidirect |
| 4. C4×(C2×D127)⋊C4 | C2 | semidirect |
| 5. C4×C22⋊Dic127 | C2 | semidirect |
| 6. C42×Dic127 | C2 | semidirect |
| 7. C22×C42×C127 | C2 | semidirect |
| 10. C4×C22⋊D127 | C4 | direct (N × H) |
| 30. C2×C4×D127 | C2×C4 | semidirect |
| 31. Dic127⋊C4 | C2×C4 | semidirect |
| 32. C22⋊Dic127 | C2×C4 | semidirect |
| 33. (C2×D127)⋊C4 | C2×C4 | semidirect |
| 36. C4×Dic127 | C2×C4 | semidirect |
| 40. C22×C4×C127 | C2×C4 | semidirect |
| 44. C42×C127 | D4 | semidirect |
| 48. C22⋊D127 | C42 | direct (N × H) |
| 69. C22×C127 | C2×C42 | semidirect |
| 75. C2×D127 | C2×C42 | semidirect |
| 77. C4×C127 | C4×D4 | semidirect |
| 80. Dic127 | C2×C42 | semidirect |
| 87. C127 | C42×D4 | semidirect |
| 90. C22×C42 | D127 | semidirect |
| 121. C22×C4 | C4×D127 | semidirect |
| 131. C42 | C22⋊D127 | direct (N × H) |
| 159. C22 | C42×D127 | semidirect |
| 167. C4 | C4×C22⋊D127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D127 | 2 |
| C2×C42×D127 | 2 |
| C4×Dic127⋊C4 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| C4×C22⋊Dic127 | 2 |
| C42×Dic127 | 2 |
| C22×C42×C127 | 2 |
| C42×D4 | 127 |