Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×Dic212 | C2 | semidirect |
| 3. C22×#11719925 | C2 | semidirect |
| 5. #16810780 | C2 | direct (N × H) |
| 6. C2×#13133140 | C2 | semidirect |
| 8. C2×#103×C53 | C2 | semidirect |
| 19. C2×Dic212 | C22 | semidirect |
| 21. C2×#11719925 | C22 | semidirect |
| 27. #13133140 | C22 | semidirect |
| 32. #103×C53 | C22 | semidirect |
| 76. C22×D53 | Q16 | semidirect |
| 115. C2×D53 | C2×Q16 | semidirect |
| 125. C2×C53 | #451 | semidirect |
| 136. C2×#103 | D53 | semidirect |
| 138. C53 | C2×#451 | semidirect |
| 161. #103 | C2×D53 | semidirect |
| 255. C2 | #16810780 | direct (N × H) |