Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
736 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 736 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 |
|---|---|---|
| 2. D53⋊#101 | C2 | direct (N × H) |
| 3. C2×#13133278 | C2 | semidirect |
| 10. #13133278 | C22 | semidirect |
| 91. C2×D53 | #101 | semidirect |
| 102. C2×C53 | C2×#101 | semidirect |
| 105. D53 | C2×#101 | semidirect |
| 110. C53 | C22×#101 | semidirect |
| 209. C2 | D53⋊#101 | direct (N × H) |