Finite Group DatabasebetaFinite Group DatabasebetaOrder 6848.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 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×#13133817 | C2 | semidirect |
| 2. C2×D4×D107 | C2 | semidirect |
| 3. #16812133 | C2 | direct (N × H) |
| 4. C2×#13133807 | C2 | semidirect |
| 5. C2×#13133806 | C2 | semidirect |
| 6. C2×#13133803 | C2 | semidirect |
| 7. C2×#13133801 | C2 | semidirect |
| 8. C2×D8×C107 | C2 | semidirect |
| 11. #13133817 | C22 | semidirect |
| 12. C2×Dic214 | C22 | semidirect |
| 17. D4×D107 | C22 | semidirect |
| 20. #13133807 | C22 | semidirect |
| 21. #13133806 | C22 | semidirect |
| 22. #13133803 | C22 | semidirect |
| 23. #13133801 | C22 | semidirect |
| 24. C2×C107⋊C8 | C22 | semidirect |
| 26. C2×D4×C107 | C22 | semidirect |
| 27. D8×C107 | C22 | semidirect |
| 28. C2×C8×C107 | C22 | semidirect |
| 38. D4×C107 | C23 | semidirect |
| 50. Dic214 | C23 | semidirect |
| 51. C8×C107 | C23 | semidirect |
| 52. C107⋊C8 | C23 | semidirect |
| 69. C2×C107 | AGL(1,ℤ/8) | semidirect |
| 73. C107 | C2×AGL(1,ℤ/8) | semidirect |
| 81. C2×D8 | D107 | semidirect |
| 93. C2×D4 | C2×D107 | semidirect |
| 99. D8 | C2×D107 | semidirect |
| 102. C2×C8 | C2×D107 | semidirect |
| 118. D4 | C22×D107 | semidirect |
| 126. C8 | C22×D107 | semidirect |
| 145. C2 | #16812133 | direct (N × H) |