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×#13133248 | C2 | semidirect |
| 3. C2×#13133206 | C2 | semidirect |
| 4. #16810799 | C2 | direct (N × H) |
| 5. C2×#13133144 | C2 | semidirect |
| 6. C2×#13133143 | C2 | semidirect |
| 7. C2×#13133133 | C2 | semidirect |
| 8. C2×#137×C53 | C2 | semidirect |
| 21. #13133248 | C22 | semidirect |
| 24. C2×#11719917 | C22 | semidirect |
| 26. #13133206 | C22 | semidirect |
| 28. C2×C4×Dic53 | C22 | semidirect |
| 29. #13133144 | C22 | semidirect |
| 30. #13133143 | C22 | semidirect |
| 31. #13133133 | C22 | semidirect |
| 33. C22×Q8×C53 | C22 | semidirect |
| 35. #137×C53 | C22 | semidirect |
| 38. C2×M16×C53 | C22 | semidirect |
| 51. C2×Q8×C53 | C23 | semidirect |
| 88. M16×C53 | C23 | semidirect |
| 94. C4×Dic53 | C23 | semidirect |
| 96. #11719917 | C23 | semidirect |
| 174. C2×C53 | #455 | semidirect |
| 180. C2×#137 | D53 | semidirect |
| 186. C53 | C2×#455 | semidirect |
| 195. C22×Q8 | C2×D53 | semidirect |
| 203. #137 | C2×D53 | semidirect |
| 209. C2×M16 | C2×D53 | semidirect |
| 238. C2×Q8 | C22×D53 | semidirect |
| 270. M16 | C22×D53 | semidirect |
| 353. C2 | #16810799 | direct (N × H) |