Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 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×M16×D53 | C2 | semidirect |
| 3. C2×#13133134 | C2 | semidirect |
| 4. C2×#13133133 | C2 | semidirect |
| 5. #100×D53 | C2 | direct (N × H) |
| 6. C2×#100×C53 | C2 | semidirect |
| 16. C2×#11719917 | C22 | semidirect |
| 19. M16×D53 | C22 | semidirect |
| 21. #13133134 | C22 | semidirect |
| 22. #13133133 | C22 | semidirect |
| 24. C2×M16×C53 | C22 | semidirect |
| 25. #100×C53 | C22 | semidirect |
| 57. M16×C53 | C23 | semidirect |
| 60. #11719917 | C23 | semidirect |
| 119. C2×D53 | #100 | direct (N × H) |
| 129. C2×C53 | C2×#100 | semidirect |
| 133. D53 | C2×#100 | direct (N × H) |
| 139. C2×#100 | D53 | direct (N × H) |
| 140. C53 | C22×#100 | semidirect |
| 155. C2×M16 | C2×D53 | semidirect |
| 159. #100 | C2×D53 | direct (N × H) |
| 194. M16 | C22×D53 | semidirect |
| 265. C2 | #100×D53 | direct (N × H) |