Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
176 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 87 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. Q8×C127⋊C8 | C2 | semidirect |
| 3. #22549629 | C2 | semidirect |
| 4. Q8⋊(C127⋊C8) | C2 | semidirect |
| 6. #22549597 | C2 | semidirect |
| 32. SD16×C127 | C8 | semidirect |
| 48. Q8×C127 | C2×C8 | semidirect |
| 60. C8×C127 | C2×C8 | semidirect |
| 78. C127 | SD16⋊C8 | semidirect |
| 104. SD16 | C127⋊C8 | semidirect |
| 121. Q8 | C2×C127⋊C8 | semidirect |
| 138. C8 | C2×C127⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C127⋊C8 | 2 |
| D4×C127⋊C8 | 2 |
| #22549629 | 2 |
| Q8⋊(C127⋊C8) | 2 |
| D4⋊(C127⋊C8) | 2 |
| #22549597 | 2 |
| C4×SD16×C127 | 2 |
| SD16⋊C8 | 127 |