Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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×#13133175 | C2 | semidirect |
| 3. #16810966 | C2 | semidirect |
| 4. #16810959 | C2 | semidirect |
| 5. #16810953 | C2 | semidirect |
| 6. #16810945 | C2 | semidirect |
| 7. #16810939 | C2 | semidirect |
| 8. #16810660 | C2 | semidirect |
| 9. #16810616 | C2 | semidirect |
| 10. C22⋊C8×D53 | C2 | semidirect |
| 11. C53×#480 | C2 | semidirect |
| 30. #13133151 | C22 | semidirect |
| 31. #13133148 | C22 | semidirect |
| 32. #13133148 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 34. #13133140 | C22 | semidirect |
| 35. #13133138 | C22 | semidirect |
| 40. #107×C53 | C22 | semidirect |
| 41. #102×C53 | C22 | semidirect |
| 151. #480 | D53 | semidirect |
| 155. C53 | #3091 | semidirect |
| 177. #107 | C2×D53 | semidirect |
| 183. #102 | C2×D53 | semidirect |