Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
544 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×Q8×Dic53 | C2 | semidirect |
| 3. #16810724 | C2 | direct (N × H) |
| 4. C2×#13133151 | C2 | semidirect |
| 5. C2×#13133141 | C2 | semidirect |
| 7. C2×#13133127 | C2 | semidirect |
| 12. Q8×Dic53 | C22 | semidirect |
| 21. #13133151 | C22 | semidirect |
| 22. #13133141 | C22 | semidirect |
| 24. #13133127 | C22 | semidirect |
| 27. C2×SD16×C53 | C4 | semidirect |
| 33. C2×Q8×C53 | C2×C4 | semidirect |
| 47. SD16×C53 | C2×C4 | semidirect |
| 48. C2×C8×C53 | C2×C4 | semidirect |
| 68. Q8×C53 | C22×C4 | semidirect |
| 87. C8×C53 | C22×C4 | semidirect |
| 107. C2×C53 | #440 | semidirect |
| 119. C53 | C2×#440 | semidirect |
| 123. C2×SD16 | Dic53 | semidirect |
| 144. C2×Q8 | C2×Dic53 | semidirect |
| 158. SD16 | C2×Dic53 | semidirect |
| 161. C2×C8 | C2×Dic53 | semidirect |
| 179. Q8 | C22×Dic53 | semidirect |
| 199. C8 | C22×Dic53 | semidirect |
| 217. C2 | #16810724 | direct (N × H) |