Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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. #16811389 | C2 | semidirect |
| 4. #16810895 | C2 | semidirect |
| 5. #16810883 | C2 | semidirect |
| 6. #16810672 | C2 | semidirect |
| 7. #16810607 | C2 | semidirect |
| 8. C2×#13133136 | C2 | semidirect |
| 9. C2×#137×C53 | C2 | semidirect |
| 26. #13133153 | C22 | semidirect |
| 27. #13133136 | C22 | semidirect |
| 28. #13133136 | C22 | semidirect |
| 29. #13133134 | C22 | semidirect |
| 34. C2×Q16×C53 | C22 | semidirect |
| 35. C2×SD16×C53 | C22 | semidirect |
| 145. C2×#137 | D53 | semidirect |
| 152. C53 | #3069 | semidirect |
| 166. C2×Q16 | C2×D53 | semidirect |
| 168. C2×SD16 | C2×D53 | semidirect |