Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×D1016 | C2 | semidirect |
| 3. #22549701 | C2 | semidirect |
| 4. #22549677 | C2 | semidirect |
| 5. #22549676 | C2 | semidirect |
| 6. C4×C127⋊C16 | C2 | semidirect |
| 7. C4×D8×C127 | C2 | semidirect |
| 10. #16861150 | C4 | direct (N × H) |
| 23. D1016 | C2×C4 | semidirect |
| 27. C127⋊C16 | C2×C4 | semidirect |
| 31. D8×C127 | C2×C4 | semidirect |
| 62. C4×C127 | D16 | semidirect |
| 72. C127 | C4×D16 | semidirect |
| 75. C4×D8 | D127 | semidirect |
| 99. D8 | C4×D127 | semidirect |
| 135. C4 | #16861150 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861150 | 2 |
| C4×D1016 | 2 |
| #22549701 | 2 |
| #22549677 | 2 |
| #22549676 | 2 |
| C4×C127⋊C16 | 2 |
| C4×D8×C127 | 2 |
| C4×D16 | 127 |