Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 103 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×#14523249 | C2 | semidirect |
| 2. C2×#14523247 | C2 | semidirect |
| 3. #16861230 | C2 | direct (N × H) |
| 4. C2×#14523238 | C2 | semidirect |
| 5. C2×#14523237 | C2 | semidirect |
| 6. C2×#14523233 | C2 | semidirect |
| 7. C2×C8×D127 | C2 | semidirect |
| 8. C2×SD16×C127 | C2 | semidirect |
| 10. #14523249 | C22 | semidirect |
| 12. #14523247 | C22 | semidirect |
| 20. #14523238 | C22 | semidirect |
| 21. #14523237 | C22 | semidirect |
| 22. #14523233 | C22 | semidirect |
| 24. C8×D127 | C22 | semidirect |
| 27. SD16×C127 | C22 | semidirect |
| 65. C2×C127 | #135 | semidirect |
| 69. C127 | C2×#135 | semidirect |
| 76. C2×SD16 | D127 | semidirect |
| 94. SD16 | C2×D127 | semidirect |
| 137. C2 | #16861230 | direct (N × H) |