Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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. #16861140 | C2 | semidirect |
| 4. #16861133 | C2 | semidirect |
| 6. C4×C127⋊C8 | C2 | semidirect |
| 7. C4×Q8×C127 | C2 | semidirect |
| 10. #14523235 | C4 | direct (N × H) |
| 26. C127⋊C8 | C2×C4 | semidirect |
| 28. Q8×C127 | C2×C4 | semidirect |
| 41. C4×C127 | SD16 | semidirect |
| 49. C127 | C4×SD16 | semidirect |
| 52. C4×Q8 | D127 | semidirect |
| 72. Q8 | C4×D127 | semidirect |
| 92. C4 | #14523235 | direct (N × H) |