Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 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. Q8×Dic106 | C2 | semidirect |
| 3. #16811021 | C2 | semidirect |
| 4. #16811020 | C2 | semidirect |
| 7. #16810908 | C2 | semidirect |
| 8. #16810906 | C2 | semidirect |
| 9. C8×Dic106 | C2 | semidirect |
| 51. SD16×C53 | Q8 | semidirect |
| 75. Q8×C53 | C2×Q8 | semidirect |
| 94. Dic106 | SD16 | direct (N × H) |
| 96. C8×C53 | C2×Q8 | semidirect |
| 129. C53 | Q8×SD16 | semidirect |
| 169. SD16 | Dic106 | direct (N × H) |
| 198. Q8 | C2×Dic106 | semidirect |
| 215. C8 | C2×Dic106 | semidirect |