Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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. #41×D167 | C2 | semidirect |
| 2. C2×D4×D167 | C2 | semidirect |
| 3. #19128860 | C2 | semidirect |
| 4. #19128859 | C2 | semidirect |
| 5. #19128858 | C2 | semidirect |
| 6. #19128857 | C2 | semidirect |
| 7. #19128856 | C2 | semidirect |
| 8. SD16×D167 | C2 | semidirect |
| 9. D8×D167 | C2 | semidirect |
| 10. M16×D167 | C2 | semidirect |
| 11. AGL(1,ℤ/8)×C167 | C2 | semidirect |
| 13. #14581951 | C22 | semidirect |
| 15. #14581950 | C22 | semidirect |
| 17. #14581949 | C22 | semidirect |
| 18. Q8×D167 | C22 | semidirect |
| 19. C2×D668 | C22 | semidirect |
| 25. D4×D167 | C22 | semidirect |
| 26. D4×D167 | C22 | semidirect |
| 29. #14581939 | C22 | semidirect |
| 30. #14581938 | C22 | semidirect |
| 31. #14581937 | C22 | semidirect |
| 32. D1336 | C22 | semidirect |
| 33. #14581935 | C22 | semidirect |
| 34. #14581935 | C22 | semidirect |
| 35. #14581934 | C22 | semidirect |
| 36. #14581933 | C22 | semidirect |
| 37. C8×D167 | C22 | semidirect |
| 38. #41×C167 | C22 | semidirect |
| 39. C2×D4×C167 | C22 | semidirect |
| 40. SD16×C167 | C22 | semidirect |
| 41. D8×C167 | C22 | semidirect |
| 42. M16×C167 | C22 | semidirect |
| 50. Dic334 | C23 | semidirect |
| 54. D668 | C23 | semidirect |
| 69. C167⋊C8 | C23 | semidirect |
| 71. Q8×C167 | C23 | semidirect |
| 75. D4×C167 | C23 | semidirect |
| 78. C8×C167 | C23 | semidirect |
| 105. D167 | AGL(1,ℤ/8) | direct (N × H) |
| 106. C167 | C2×AGL(1,ℤ/8) | semidirect |
| 115. AGL(1,ℤ/8) | D167 | direct (N × H) |
| 125. #41 | C2×D167 | semidirect |
| 135. C2×D4 | C2×D167 | semidirect |
| 141. SD16 | C2×D167 | semidirect |
| 145. D8 | C2×D167 | semidirect |
| 148. M16 | C2×D167 | semidirect |
| 159. Q8 | C22×D167 | semidirect |
| 172. D4 | C22×D167 | semidirect |
| 185. C8 | C22×D167 | semidirect |