Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×SD16×D53 | C2 | semidirect |
| 2. Q8×D212 | C2 | semidirect |
| 4. #16810996 | C2 | semidirect |
| 5. #16810853 | C2 | semidirect |
| 6. #16810828 | C2 | semidirect |
| 7. #16810823 | C2 | semidirect |
| 8. #16810775 | C2 | semidirect |
| 9. #16810763 | C2 | semidirect |
| 10. C8×D212 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 12. C2×Q8×D53 | C22 | semidirect |
| 15. C2×#11719913 | C22 | semidirect |
| 16. C2×#11719913 | C22 | semidirect |
| 18. C2×#11719924 | C22 | semidirect |
| 20. C2×C8×D53 | C22 | semidirect |
| 22. #13133217 | C22 | semidirect |
| 25. #13133197 | C22 | semidirect |
| 31. C4⋊#88322 | C22 | semidirect |
| 32. #13133140 | C22 | semidirect |
| 33. #13133137 | C22 | semidirect |
| 34. #13133129 | C22 | semidirect |
| 36. C4×Q8×C53 | C22 | semidirect |
| 38. #106×C53 | C22 | semidirect |
| 39. #103×C53 | C22 | semidirect |
| 41. C4×C8×C53 | C22 | semidirect |
| 61. SD16×C53 | D4 | semidirect |
| 90. Q8×C53 | C2×D4 | semidirect |
| 108. D212 | SD16 | direct (N × H) |
| 116. C8×C53 | C2×D4 | semidirect |
| 128. C2×D53 | C2×SD16 | semidirect |
| 133. C4×C53 | C2×SD16 | semidirect |
| 154. C4×SD16 | D53 | semidirect |
| 156. C53 | D4×SD16 | semidirect |
| 175. C4×Q8 | C2×D53 | semidirect |
| 179. #106 | C2×D53 | semidirect |
| 182. #103 | C2×D53 | semidirect |
| 186. C4×C8 | C2×D53 | semidirect |
| 210. SD16 | D212 | direct (N × H) |
| 238. Q8 | C2×D212 | semidirect |
| 262. C8 | C2×D212 | semidirect |
| 280. C4 | SD16×D53 | semidirect |