Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #16811104 | C2 | semidirect |
| 3. C2×#13133143 | C2 | semidirect |
| 4. #16810629 | C2 | semidirect |
| 5. #16810524 | C2 | semidirect |
| 6. #16810384 | C2 | semidirect |
| 7. C53×#343 | C2 | semidirect |
| 11. #13133245 | C4 | semidirect |
| 42. C2×D212 | C2×C4 | semidirect |
| 50. M16×C53 | C2×C4 | semidirect |
| 95. D212 | C22⋊C4 | semidirect |
| 100. Dic106 | C22⋊C4 | semidirect |
| 138. #343 | D53 | semidirect |
| 140. C53 | #1883 | semidirect |
| 185. M16 | C4×D53 | semidirect |