Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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×Q8×Dic53 | C2 | semidirect |
| 4. #16810708 | C2 | direct (N × H) |
| 5. C2×#13133148 | C2 | semidirect |
| 7. C2×C8×Dic53 | C2 | semidirect |
| 8. C2×#103×C53 | C2 | semidirect |
| 11. C2×#11719924 | C4 | semidirect |
| 15. Q8×Dic53 | C22 | semidirect |
| 23. #13133148 | C22 | semidirect |
| 25. C8×Dic53 | C22 | semidirect |
| 29. #103×C53 | C22 | semidirect |
| 33. C2×Q8×C53 | C2×C4 | semidirect |
| 51. #11719924 | C2×C4 | semidirect |
| 59. C2×#88322 | C2×C4 | semidirect |
| 68. Q8×C53 | C22×C4 | semidirect |
| 80. C2×Dic53 | SD16 | semidirect |
| 88. #88322 | C22×C4 | semidirect |
| 104. Dic53 | C2×SD16 | semidirect |
| 106. C2×C53 | C4×SD16 | semidirect |
| 116. C2×#103 | D53 | semidirect |
| 119. C53 | C2×C4×SD16 | semidirect |
| 138. #103 | C2×D53 | semidirect |
| 144. C2×Q8 | C4×D53 | semidirect |
| 179. Q8 | C2×C4×D53 | semidirect |
| 217. C2 | #16810708 | direct (N × H) |