Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14523233 | C2 | semidirect |
| 2. #16861183 | C2 | semidirect |
| 3. #16861130 | C2 | semidirect |
| 4. C22⋊(C127⋊C8) | C2 | semidirect |
| 5. C22×D4×C127 | C2 | semidirect |
| 6. C2×D508 | C22 | semidirect |
| 9. C2×C127⋊C8 | C22 | semidirect |
| 10. C4⋊Dic127 | C22 | semidirect |
| 29. D4×C127 | D4 | semidirect |
| 39. C22×C127 | D8 | semidirect |
| 53. C127 | #447 | semidirect |
| 55. C22×D4 | D127 | semidirect |
| 81. D4 | C22⋊D127 | semidirect |
| 96. C22 | #14523233 | semidirect |