Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 74 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. #16811628 | C2 | semidirect |
| 2. C2×#13133282 | C2 | semidirect |
| 3. C2×#13133281 | C2 | semidirect |
| 4. C42×#6157 | C2 | semidirect |
| 14. #13133215 | C4 | semidirect |
| 15. #13133213 | C4 | semidirect |
| 16. #13133205 | C4 | semidirect |
| 20. #124×C53 | C4 | semidirect |
| 40. C4×#6157 | D4 | semidirect |
| 87. Dic53 | #104 | semidirect |
| 101. C53 | #1962 | semidirect |
| 108. #124 | #6157 | semidirect |