Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
752 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 357 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. C4×Dic127⋊C4 | C2 | semidirect |
| 5. #22549722 | C2 | semidirect |
| 6. C42×Dic127 | C2 | semidirect |
| 7. C43×C127 | C2 | semidirect |
| 10. #16861166 | C4 | direct (N × H) |
| 17. C42×D127 | C4 | semidirect |
| 30. Dic127⋊C4 | C2×C4 | semidirect |
| 35. C4×Dic127 | C2×C4 | semidirect |
| 41. C42×C127 | C2×C4 | semidirect |
| 52. C4×D127 | C42 | semidirect |
| 68. C4×C127 | #117 | semidirect |
| 77. C127 | C4×#117 | semidirect |
| 84. C43 | D127 | semidirect |
| 118. C42 | C4×D127 | semidirect |
| 148. C4 | #16861166 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861166 | 2 |
| C2×C42×D127 | 2 |
| C4×Dic127⋊C4 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| #22549722 | 2 |
| C42×Dic127 | 2 |
| C43×C127 | 2 |
| C4×#117 | 127 |