Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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. C2×#13133156 | C2 | semidirect |
| 3. #107×D53 | C2 | semidirect |
| 4. #16810427 | C2 | semidirect |
| 5. #16810425 | C2 | semidirect |
| 6. #16810423 | C2 | semidirect |
| 7. C53×#358 | C2 | semidirect |
| 10. #13133240 | C4 | semidirect |
| 31. Q16×C53 | C2×C4 | semidirect |
| 39. D424 | C2×C4 | semidirect |
| 86. #358 | D53 | semidirect |
| 89. C53 | #2139 | semidirect |
| 113. Q16 | C4×D53 | semidirect |