Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×#13133248 | C2 | semidirect |
| 3. #16811002 | C2 | semidirect |
| 4. #16810879 | C2 | semidirect |
| 5. #16810833 | C2 | semidirect |
| 6. #16810825 | C2 | semidirect |
| 7. #16810783 | C2 | semidirect |
| 8. #16810779 | C2 | semidirect |
| 9. C4×#11719924 | C2 | semidirect |
| 10. #16810701 | C2 | semidirect |
| 11. D4×Q8×C53 | C2 | semidirect |
| 72. #11719924 | D4 | semidirect |
| 124. C4×C53 | #137 | semidirect |
| 136. D4×Q8 | D53 | semidirect |
| 146. C53 | #3276 | semidirect |
| 261. C4 | #13133248 | semidirect |