Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #19128878 | C2 | semidirect |
| 2. #19128877 | C2 | semidirect |
| 3. #19128860 | C2 | semidirect |
| 4. #19128859 | C2 | semidirect |
| 5. #19128856 | C2 | semidirect |
| 6. #19128853 | C2 | semidirect |
| 7. #19128852 | C2 | semidirect |
| 8. C2×#14581935 | C2 | semidirect |
| 9. D8×D167 | C2 | semidirect |
| 10. #19128840 | C2 | semidirect |
| 11. AGL(1,ℤ/8)×C167 | C2 | semidirect |
| 12. #14581951 | C22 | semidirect |
| 15. #14581950 | C22 | semidirect |
| 17. #14581949 | C22 | semidirect |
| 19. C2×D668 | C22 | semidirect |
| 23. D4×D167 | C22 | semidirect |
| 24. D4×D167 | C22 | semidirect |
| 25. #14581940 | C22 | semidirect |
| 26. #14581939 | C22 | semidirect |
| 27. #14581938 | C22 | semidirect |
| 28. #14581937 | C22 | semidirect |
| 29. D1336 | C22 | semidirect |
| 30. #14581935 | C22 | semidirect |
| 31. #14581935 | C22 | semidirect |
| 32. #14581935 | C22 | semidirect |
| 33. #14581933 | C22 | semidirect |
| 34. C2×C167⋊C8 | C22 | semidirect |
| 35. C8×D167 | C22 | semidirect |
| 36. #41×C167 | C22 | semidirect |
| 37. C2×D4×C167 | C22 | semidirect |
| 38. SD16×C167 | C22 | semidirect |
| 39. D8×C167 | C22 | semidirect |
| 40. M16×C167 | C22 | semidirect |
| 93. C167 | #576 | semidirect |
| 100. AGL(1,ℤ/8) | D167 | semidirect |
| 112. #41 | C2×D167 | semidirect |
| 120. C2×D4 | C2×D167 | semidirect |
| 125. SD16 | C2×D167 | semidirect |
| 130. D8 | C2×D167 | semidirect |
| 132. M16 | C2×D167 | semidirect |