Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. Q8×D212 | C2 | semidirect |
| 3. #16810974 | C2 | semidirect |
| 4. #16810955 | C2 | semidirect |
| 5. #16810908 | C2 | semidirect |
| 6. #16810851 | C2 | semidirect |
| 7. #16810828 | C2 | semidirect |
| 8. #16810760 | C2 | semidirect |
| 9. C8×D212 | C2 | semidirect |
| 10. #103×D53 | C2 | semidirect |
| 11. C4×SD16×C53 | C2 | semidirect |
| 80. Q8×C53 | #41 | semidirect |
| 94. D212 | SD16 | semidirect |
| 137. C4×SD16 | D53 | semidirect |
| 140. C53 | #3298 | semidirect |
| 213. Q8 | #11719945 | semidirect |