Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 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. #19128880 | C2 | semidirect |
| 2. #19128878 | C2 | semidirect |
| 3. #19128864 | C2 | semidirect |
| 4. #19128860 | C2 | semidirect |
| 5. #19128859 | C2 | semidirect |
| 6. #19128855 | C2 | semidirect |
| 7. #19128852 | C2 | semidirect |
| 8. C2×#14581937 | C2 | semidirect |
| 9. SD16×D167 | C2 | semidirect |
| 10. #19128840 | C2 | semidirect |
| 11. #137×C167 | C2 | semidirect |
| 14. #14581951 | C22 | semidirect |
| 18. #14581950 | C22 | semidirect |
| 20. Q8×D167 | C22 | semidirect |
| 25. #14581940 | C22 | semidirect |
| 26. #14581939 | C22 | semidirect |
| 27. #14581938 | C22 | semidirect |
| 28. #14581937 | C22 | semidirect |
| 29. #14581937 | C22 | semidirect |
| 30. #14581937 | C22 | semidirect |
| 31. D1336 | C22 | semidirect |
| 32. #14581935 | C22 | semidirect |
| 33. #14581933 | C22 | semidirect |
| 34. C2×C167⋊C8 | C22 | semidirect |
| 35. C8×D167 | C22 | semidirect |
| 37. C2×Q8×C167 | C22 | semidirect |
| 38. Q16×C167 | C22 | semidirect |
| 39. SD16×C167 | C22 | semidirect |
| 40. M16×C167 | C22 | semidirect |
| 90. C167 | #577 | semidirect |
| 95. #137 | D167 | semidirect |
| 113. C2×Q8 | C2×D167 | semidirect |
| 119. Q16 | C2×D167 | semidirect |
| 125. SD16 | C2×D167 | semidirect |
| 129. M16 | C2×D167 | semidirect |