Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
272 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 74 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×D53⋊C16 | C2 | semidirect |
| 2. C2×#13133286 | C2 | semidirect |
| 3. #16811535 | C2 | direct (N × H) |
| 7. D53⋊C16 | C22 | semidirect |
| 10. #13133286 | C22 | semidirect |
| 12. C2×D424 | C4 | semidirect |
| 16. D8×D53 | C4 | semidirect |
| 19. C2×D8×C53 | C4 | semidirect |
| 33. D8×C53 | C2×C4 | semidirect |
| 39. D424 | C2×C4 | semidirect |
| 89. C2×C53 | #357 | semidirect |
| 92. D53 | #357 | semidirect |
| 99. C53 | C2×#357 | semidirect |
| 107. C2×D8 | #6157 | semidirect |
| 130. D8 | C2×#6157 | semidirect |
| 187. C2 | #16811535 | direct (N × H) |