Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#11719925 | C2 | semidirect |
| 3. #16811002 | C2 | semidirect |
| 4. #16810862 | C2 | semidirect |
| 5. #16810833 | C2 | semidirect |
| 6. #16810830 | C2 | semidirect |
| 7. #16810779 | C2 | semidirect |
| 8. #16810778 | C2 | semidirect |
| 9. C4×#11719925 | C2 | semidirect |
| 71. #11719925 | D4 | direct (N × H) |
| 88. D4×C53 | Q16 | semidirect |
| 113. C22×C53 | C2×Q16 | semidirect |
| 120. C4×C53 | C2×Q16 | semidirect |
| 142. C53 | D4×Q16 | semidirect |
| 224. D4 | #11719925 | direct (N × H) |
| 244. C22 | C2×#11719925 | semidirect |
| 254. C4 | C2×#11719925 | semidirect |