Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
992 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 309 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. C22×#11719917 | C2 | semidirect |
| 2. C2×#13133134 | C2 | direct (N × H) |
| 5. C2×#11719917 | C22 | semidirect |
| 7. #13133134 | C22 | direct (N × H) |
| 30. #11719917 | C23 | semidirect |
| 57. C22×C53 | #100 | semidirect |
| 67. C2×C53 | C2×#100 | semidirect |
| 72. C53 | C22×#100 | semidirect |
| 126. C22 | #13133134 | direct (N × H) |
| 135. C2 | C2×#13133134 | direct (N × H) |