Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
756 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 213 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. #16810606 | C2 | direct (N × H) |
| 4. C2×#13133136 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. C2×#101×C53 | C2 | semidirect |
| 19. M16×D53 | C22 | semidirect |
| 21. #13133136 | C22 | semidirect |
| 22. #13133133 | C22 | semidirect |
| 25. #101×C53 | C22 | semidirect |
| 116. C2×C53 | #413 | semidirect |
| 124. C2×#101 | D53 | semidirect |
| 126. C53 | C2×#413 | semidirect |
| 144. #101 | C2×D53 | semidirect |
| 237. C2 | #16810606 | direct (N × H) |