Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 2. #19128791 | C2 | semidirect |
| 3. #19128790 | C2 | semidirect |
| 4. #19128789 | C2 | semidirect |
| 5. #19128788 | C2 | semidirect |
| 6. C4⋊C4×D167 | C2 | semidirect |
| 8. C42×D167 | C2 | semidirect |
| 9. #117×C167 | C2 | semidirect |
| 12. C2×C4×D167 | C4 | semidirect |
| 18. C4⋊Dic167 | C22 | semidirect |
| 19. Dic167⋊C4 | C22 | semidirect |
| 22. C4×Dic167 | C22 | semidirect |
| 23. C4×Dic167 | C22 | semidirect |
| 25. C4⋊C4×C167 | C22 | semidirect |
| 27. C42×C167 | C22 | semidirect |
| 32. C2×Dic167 | C2×C4 | semidirect |
| 39. C4×D167 | C2×C4 | semidirect |
| 40. C4×D167 | C2×C4 | semidirect |
| 42. C2×C4×C167 | C2×C4 | semidirect |
| 64. D167 | #117 | direct (N × H) |
| 65. C167 | C2×#117 | semidirect |
| 72. #117 | D167 | direct (N × H) |
| 87. C4⋊C4 | C2×D167 | semidirect |
| 93. C42 | C2×D167 | semidirect |
| 108. C2×C4 | C4×D167 | semidirect |