Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
992 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 210 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⋊M16 | C2 | semidirect |
| 2. D53⋊#100 | C2 | direct (N × H) |
| 3. C2×#13133277 | C2 | semidirect |
| 7. D53⋊M16 | C22 | semidirect |
| 8. C2×#11719940 | C22 | semidirect |
| 10. #13133277 | C22 | semidirect |
| 51. #11719940 | C23 | semidirect |
| 108. C2×D53 | #100 | semidirect |
| 118. C2×C53 | C2×#100 | semidirect |
| 122. D53 | C2×#100 | semidirect |
| 127. C53 | C22×#100 | semidirect |
| 243. C2 | D53⋊#100 | direct (N × H) |