Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. #16811030 | C2 | direct (N × H) |
| 38. C2×C8×C53 | Q8 | semidirect |
| 53. C2×#88322 | Q8 | semidirect |
| 73. C8×C53 | C2×Q8 | semidirect |
| 74. #88322 | C2×Q8 | semidirect |
| 89. C2×C53 | #501 | semidirect |
| 101. C53 | C2×#501 | semidirect |
| 133. C2×C8 | Dic106 | semidirect |
| 167. C8 | C2×Dic106 | semidirect |
| 181. C2 | #16811030 | direct (N × H) |