Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. #16810428 | C2 | semidirect |
| 5. #16810427 | C2 | semidirect |
| 6. #16810426 | C2 | semidirect |
| 7. C53×#358 | C2 | semidirect |
| 12. Q16×D53 | C4 | semidirect |
| 31. Q16×C53 | C2×C4 | semidirect |
| 39. Dic212 | C2×C4 | semidirect |
| 78. D53 | #358 | direct (N × H) |
| 85. #358 | D53 | direct (N × H) |
| 86. C53 | C2×#358 | semidirect |
| 113. Q16 | C4×D53 | semidirect |