Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#14581934 | C2 | semidirect |
| 3. #19128760 | C2 | direct (N × H) |
| 4. C2×C42×C167 | C2 | semidirect |
| 7. #14581950 | C4 | semidirect |
| 9. C2×Dic334 | C4 | semidirect |
| 10. C2×D668 | C4 | semidirect |
| 14. #14581934 | C22 | semidirect |
| 19. C42×C167 | C22 | semidirect |
| 22. Dic334 | C2×C4 | semidirect |
| 24. D668 | C2×C4 | semidirect |
| 54. C2×C167 | #104 | semidirect |
| 57. C167 | C2×#104 | semidirect |
| 61. C2×C42 | D167 | semidirect |
| 77. C42 | C2×D167 | semidirect |
| 113. C2 | #19128760 | direct (N × H) |