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 |
|---|---|---|
| 2. C4×Dic254 | C2 | semidirect |
| 4. #16861141 | C2 | semidirect |
| 5. #16861134 | C2 | semidirect |
| 7. C4×C8×C127 | C2 | semidirect |
| 11. #14523237 | C4 | direct (N × H) |
| 22. Dic254 | C2×C4 | semidirect |
| 33. C8×C127 | C2×C4 | semidirect |
| 39. C4×C127 | SD16 | semidirect |
| 49. C127 | C4×SD16 | semidirect |
| 57. C4×C8 | D127 | semidirect |
| 83. C8 | C4×D127 | semidirect |
| 92. C4 | #14523237 | direct (N × H) |