Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
412 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 170 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. #16811647 | C2 | direct (N × H) |
| 2. C2×#13133284 | C2 | semidirect |
| 3. C2×C4⋊#88324 | C2 | semidirect |
| 6. C2×#13133272 | C2 | semidirect |
| 7. C2×C4×#88324 | C2 | semidirect |
| 13. #13133284 | C22 | semidirect |
| 14. C4⋊#88324 | C22 | semidirect |
| 17. #13133272 | C22 | semidirect |
| 18. C4×#88324 | C22 | semidirect |
| 99. C2×C53 | #433 | semidirect |
| 111. C53 | C2×#433 | semidirect |
| 201. C2 | #16811647 | direct (N × H) |