Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
224 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 62 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×#13133292 | C2 | semidirect |
| 2. #16811633 | C2 | semidirect |
| 3. #16811540 | C2 | semidirect |
| 4. #16811539 | C2 | semidirect |
| 8. #13133292 | C22 | semidirect |
| 11. #13133285 | C22 | semidirect |
| 14. #13133239 | C4 | semidirect |
| 18. Q16×D53 | C4 | semidirect |
| 20. D8×D53 | C4 | semidirect |
| 22. #135×C53 | C4 | semidirect |
| 108. C53 | #2145 | semidirect |
| 115. #135 | #6157 | semidirect |