Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
232 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 66 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×#13133292 | C2 | semidirect |
| 2. C2×#13133285 | C2 | semidirect |
| 3. #16811540 | C2 | direct (N × H) |
| 7. #13133292 | C22 | semidirect |
| 10. #13133285 | C22 | semidirect |
| 14. #13133240 | C4 | semidirect |
| 17. C2×D424 | C4 | semidirect |
| 19. C2×Q16×C53 | C4 | semidirect |
| 33. Q16×C53 | C2×C4 | semidirect |
| 39. D424 | C2×C4 | semidirect |
| 81. C2×C53 | #360 | semidirect |
| 90. C53 | C2×#360 | semidirect |
| 96. C2×Q16 | #6157 | semidirect |
| 117. Q16 | C2×#6157 | semidirect |
| 169. C2 | #16811540 | direct (N × H) |