Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 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×C4⋊C4×D53 | C2 | semidirect |
| 3. #16810940 | C2 | direct (N × H) |
| 4. C2×#13133149 | C2 | semidirect |
| 5. C2×#13133148 | C2 | semidirect |
| 6. C2×#13133138 | C2 | semidirect |
| 7. C2×#13133129 | C2 | semidirect |
| 8. C2×#102×C53 | C2 | semidirect |
| 19. C4⋊C4×D53 | C22 | semidirect |
| 21. #13133149 | C22 | semidirect |
| 22. #13133148 | C22 | semidirect |
| 23. #13133138 | C22 | semidirect |
| 24. #13133129 | C22 | semidirect |
| 28. #102×C53 | C22 | semidirect |
| 112. C2×C53 | #481 | semidirect |
| 123. C2×#102 | D53 | semidirect |
| 125. C53 | C2×#481 | semidirect |
| 144. #102 | C2×D53 | semidirect |
| 229. C2 | #16810940 | direct (N × H) |