Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133250 | C2 | semidirect |
| 3. C2×#13133247 | C2 | semidirect |
| 4. C2×#13133205 | C2 | semidirect |
| 5. #16810802 | C2 | direct (N × H) |
| 6. C2×#13133145 | C2 | semidirect |
| 7. C2×#13133133 | C2 | semidirect |
| 8. C2×#104×C53 | C2 | semidirect |
| 16. C22×Dic106 | C22 | semidirect |
| 22. #13133250 | C22 | semidirect |
| 24. #13133247 | C22 | semidirect |
| 29. C2×#11719917 | C22 | semidirect |
| 31. #13133205 | C22 | semidirect |
| 33. #13133145 | C22 | semidirect |
| 34. #13133133 | C22 | semidirect |
| 36. C2×M16×C53 | C22 | semidirect |
| 37. C2×C42×C53 | C22 | semidirect |
| 38. #104×C53 | C22 | semidirect |
| 84. C2×Dic106 | C23 | semidirect |
| 86. M16×C53 | C23 | semidirect |
| 89. C42×C53 | C23 | semidirect |
| 94. #11719917 | C23 | semidirect |
| 174. C2×C53 | #455 | semidirect |
| 184. C2×#104 | D53 | semidirect |
| 186. C53 | C2×#455 | semidirect |
| 209. C2×M16 | C2×D53 | semidirect |
| 213. C2×C42 | C2×D53 | semidirect |
| 215. #104 | C2×D53 | semidirect |
| 270. M16 | C22×D53 | semidirect |
| 275. C42 | C22×D53 | semidirect |
| 353. C2 | #16810802 | direct (N × H) |