Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#13133139 | C2 | semidirect |
| 3. C2×#13133138 | C2 | semidirect |
| 4. C2×#13133137 | C2 | semidirect |
| 5. C2×#13133127 | C2 | semidirect |
| 6. #16810488 | C2 | semidirect |
| 7. C2×#102×C53 | C2 | semidirect |
| 12. #13133213 | C4 | semidirect |
| 47. C2×C8×C53 | D4 | semidirect |
| 56. C2×#88322 | D4 | semidirect |
| 126. C2×#102 | D53 | semidirect |
| 129. C53 | #1961 | semidirect |
| 172. C2×C8 | C22⋊D53 | semidirect |