Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×Q16×D53 | C2 | semidirect |
| 4. #16810880 | C2 | semidirect |
| 5. #16810879 | C2 | semidirect |
| 6. #16810865 | C2 | semidirect |
| 7. #16810864 | C2 | semidirect |
| 8. #16810861 | C2 | semidirect |
| 9. #16810660 | C2 | semidirect |
| 10. #16810630 | C2 | semidirect |
| 11. C53×#467 | C2 | semidirect |
| 146. #467 | D53 | semidirect |
| 149. C53 | #3059 | semidirect |