Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 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×#13133818 | C2 | semidirect |
| 2. C22×D428 | C2 | semidirect |
| 3. #16812137 | C2 | direct (N × H) |
| 4. C2×#13133807 | C2 | semidirect |
| 5. C2×D856 | C2 | semidirect |
| 6. C2×M16×C107 | C2 | semidirect |
| 9. #13133818 | C22 | semidirect |
| 10. C2×Dic214 | C22 | semidirect |
| 14. C2×D428 | C22 | semidirect |
| 15. C2×D428 | C22 | semidirect |
| 18. #13133807 | C22 | semidirect |
| 19. D856 | C22 | semidirect |
| 21. M16×C107 | C22 | semidirect |
| 22. C2×C8×C107 | C22 | semidirect |
| 38. D428 | C23 | semidirect |
| 41. Dic214 | C23 | semidirect |
| 42. C8×C107 | C23 | semidirect |
| 56. C2×C107 | AGL(1,ℤ/8) | semidirect |
| 60. C107 | C2×AGL(1,ℤ/8) | semidirect |
| 67. C2×M16 | D107 | semidirect |
| 82. M16 | C2×D107 | semidirect |
| 83. C2×C8 | C2×D107 | semidirect |
| 103. C8 | C22×D107 | semidirect |
| 119. C2 | #16812137 | direct (N × H) |