Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
112 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 37 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. Q32×D127 | C2 | semidirect |
| 3. #22549715 | C2 | semidirect |
| 4. #22549714 | C2 | semidirect |
| 5. #22549713 | C2 | semidirect |
| 6. C32×D127 | C2 | semidirect |
| 7. SD64×C127 | C2 | semidirect |
| 10. Dic1016 | C22 | semidirect |
| 15. C127⋊C32 | C22 | semidirect |
| 16. Q32×C127 | C22 | semidirect |
| 18. C32×C127 | C22 | semidirect |
| 52. D127 | SD64 | direct (N × H) |
| 54. C127 | C2×SD64 | semidirect |
| 60. SD64 | D127 | direct (N × H) |
| 66. Q32 | C2×D127 | semidirect |
| 72. C32 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×D127 | 2 |
| D16×D127 | 2 |
| #22549715 | 2 |
| #22549714 | 2 |
| #22549713 | 2 |
| C32×D127 | 2 |
| SD64×C127 | 2 |
| C2×SD64 | 127 |