Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 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. M16×D167 | C2 | semidirect |
| 3. C42×D167 | C2 | semidirect |
| 4. #19128760 | C2 | semidirect |
| 5. #19128759 | C2 | semidirect |
| 6. #19128758 | C2 | semidirect |
| 7. #104×C167 | C2 | semidirect |
| 8. #14581951 | C4 | semidirect |
| 12. #14581949 | C4 | semidirect |
| 13. Q8×D167 | C4 | semidirect |
| 15. D4×D167 | C4 | semidirect |
| 19. #14581934 | C22 | semidirect |
| 23. C4×Dic167 | C22 | semidirect |
| 25. M16×C167 | C22 | semidirect |
| 26. C42×C167 | C22 | semidirect |
| 30. Dic334 | C2×C4 | semidirect |
| 32. D668 | C2×C4 | semidirect |
| 48. Q8×C167 | C2×C4 | semidirect |
| 50. D4×C167 | C2×C4 | semidirect |
| 75. D167 | #104 | direct (N × H) |
| 76. C167 | C2×#104 | semidirect |
| 84. #104 | D167 | direct (N × H) |
| 99. M16 | C2×D167 | semidirect |
| 103. C42 | C2×D167 | semidirect |
| 108. Q8 | C4×D167 | semidirect |
| 115. D4 | C4×D167 | semidirect |