Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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. #19128827 | C2 | semidirect |
| 2. #19128827 | C2 | semidirect |
| 3. #19128821 | C2 | semidirect |
| 4. #19128817 | C2 | semidirect |
| 5. #19128817 | C2 | semidirect |
| 6. #19128816 | C2 | semidirect |
| 7. #19128808 | C2 | semidirect |
| 9. #19128794 | C2 | semidirect |
| 10. C4×C22⋊D167 | C2 | semidirect |
| 11. #19128790 | C2 | semidirect |
| 12. #19128788 | C2 | semidirect |
| 13. C2×(C2×D167)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D167 | C2 | semidirect |
| 15. C22⋊Q8×C167 | C2 | semidirect |
| 23. C2×C4×D167 | C22 | semidirect |
| 24. C4⋊Dic167 | C22 | semidirect |
| 25. C4⋊Dic167 | C22 | semidirect |
| 26. Dic167⋊C4 | C22 | semidirect |
| 27. Dic167⋊C4 | C22 | semidirect |
| 28. Dic167⋊C4 | C22 | semidirect |
| 38. (C2×D167)⋊C4 | C22 | semidirect |
| 39. (C2×D167)⋊C4 | C22 | semidirect |
| 40. (C2×D167)⋊C4 | C22 | semidirect |
| 41. C4×Dic167 | C22 | semidirect |
| 42. C4×Dic167 | C22 | semidirect |
| 43. C4×Dic167 | C22 | semidirect |
| 44. C2×Q8×C167 | C22 | semidirect |
| 46. C4⋊C4×C167 | C22 | semidirect |
| 47. C4⋊C4×C167 | C22 | semidirect |
| 48. C4⋊C4×C167 | C22 | semidirect |
| 110. C167 | #551 | semidirect |
| 119. C22⋊Q8 | D167 | semidirect |
| 128. C2×Q8 | C2×D167 | semidirect |
| 142. C4⋊C4 | C2×D167 | semidirect |
| 143. C4⋊C4 | C2×D167 | semidirect |
| 144. C4⋊C4 | C2×D167 | semidirect |