Finite Group DatabasebetaFinite Group DatabasebetaOrder 8128.
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#14523235 | C2 | semidirect |
| 3. #16861185 | C2 | semidirect |
| 4. #16861131 | C2 | semidirect |
| 5. #16861130 | C2 | semidirect |
| 6. (C2×D127)⋊C8 | C2 | semidirect |
| 7. C2×SD16×C127 | C2 | semidirect |
| 15. C2×C127⋊C8 | C22 | semidirect |
| 16. C4⋊Dic127 | C22 | semidirect |
| 19. C2×Q8×C127 | C22 | semidirect |
| 22. C2×C8×C127 | C22 | semidirect |
| 54. C2×D127 | SD16 | semidirect |
| 66. C127 | #450 | semidirect |
| 70. C2×SD16 | D127 | semidirect |
| 76. C2×Q8 | C2×D127 | semidirect |
| 86. C2×C8 | C2×D127 | semidirect |