Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16810936 | C2 | semidirect |
| 3. #16810918 | C2 | semidirect |
| 4. #16810823 | C2 | semidirect |
| 5. #16810762 | C2 | semidirect |
| 6. #16810721 | C2 | semidirect |
| 7. #16810680 | C2 | semidirect |
| 8. C2×C4×Q8×C53 | C2 | semidirect |
| 68. Q8×C53 | #41 | semidirect |
| 113. C2×C4×Q8 | D53 | semidirect |
| 120. C53 | #3112 | semidirect |
| 181. Q8 | #11719945 | semidirect |