Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 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. C4×Dic334 | C2 | semidirect |
| 3. #19128797 | C2 | semidirect |
| 4. D4×Dic167 | C2 | semidirect |
| 5. C4×C22⋊D167 | C2 | semidirect |
| 6. (C22⋊D167)⋊C4 | C2 | semidirect |
| 7. #19128790 | C2 | semidirect |
| 8. #19128788 | C2 | semidirect |
| 9. C2×C4×Dic167 | C2 | semidirect |
| 10. C42×D167 | C2 | semidirect |
| 11. C4×D4×C167 | C2 | semidirect |
| 12. #14581949 | C4 | direct (N × H) |
| 37. Dic334 | C2×C4 | semidirect |
| 38. C22⋊D167 | C2×C4 | semidirect |
| 40. C2×Dic167 | C2×C4 | semidirect |
| 48. C4×D167 | C2×C4 | semidirect |
| 50. D4×C167 | C2×C4 | semidirect |
| 66. C4×C167 | #41 | semidirect |
| 71. Dic167 | #41 | semidirect |
| 77. C167 | C4×#41 | semidirect |
| 85. C4×D4 | D167 | semidirect |
| 118. D4 | C4×D167 | semidirect |
| 149. C4 | #14581949 | direct (N × H) |