Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#14523248 | C2 | semidirect |
| 2. #16861229 | C2 | direct (N × H) |
| 3. C2×#14523238 | C2 | semidirect |
| 4. C2×#14523236 | C2 | semidirect |
| 5. C2×#14523235 | C2 | semidirect |
| 6. C2×#14523233 | C2 | semidirect |
| 7. C22×C127⋊C8 | C2 | semidirect |
| 8. C2×#41×C127 | C2 | semidirect |
| 10. #14523248 | C22 | semidirect |
| 15. #14523238 | C22 | semidirect |
| 16. #14523236 | C22 | semidirect |
| 17. #14523235 | C22 | semidirect |
| 18. #14523233 | C22 | semidirect |
| 21. C2×C127⋊C8 | C22 | semidirect |
| 23. #41×C127 | C22 | semidirect |
| 66. C2×C127 | #135 | semidirect |
| 69. C127 | C2×#135 | semidirect |
| 72. C2×#41 | D127 | semidirect |
| 82. #41 | C2×D127 | semidirect |
| 137. C2 | #16861229 | direct (N × H) |