Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
220 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 81 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×#13133153 | C2 | semidirect |
| 3. #16810431 | C2 | semidirect |
| 4. C2×M32×C53 | C2 | semidirect |
| 15. #13133153 | C22 | semidirect |
| 19. C2×C16×C53 | C22 | semidirect |
| 85. C2×M32 | D53 | semidirect |
| 88. C53 | #2143 | semidirect |
| 101. C2×C16 | C2×D53 | semidirect |