Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
168 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #16810373 | C2 | semidirect |
| 4. Q8⋊#88322 | C2 | semidirect |
| 6. #16810344 | C2 | semidirect |
| 7. C53×#446 | C2 | semidirect |
| 56. C8×C53 | SD16 | semidirect |
| 78. #446 | D53 | semidirect |
| 85. C53 | #1582 | semidirect |
| 138. C8 | #11719924 | semidirect |