Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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×#13133143 | C2 | semidirect |
| 3. #16810622 | C2 | semidirect |
| 4. C2×#13133133 | C2 | semidirect |
| 5. #16810524 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 7. C53×#428 | C2 | semidirect |
| 48. M16×C53 | D4 | semidirect |
| 132. #428 | D53 | semidirect |
| 138. C53 | #2037 | semidirect |
| 181. M16 | D212 | semidirect |