Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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. C4×#11719924 | C2 | direct (N × H) |
| 4. C2×#13133148 | C2 | semidirect |
| 5. C2×#13133141 | C2 | semidirect |
| 7. C2×C4×#88322 | C2 | semidirect |
| 8. C2×C4×Q8×C53 | C2 | semidirect |
| 11. C2×#11719924 | C4 | direct (N × H) |
| 19. #13133148 | C22 | semidirect |
| 20. #13133141 | C22 | semidirect |
| 22. C4×#88322 | C22 | semidirect |
| 25. C4×Q8×C53 | C22 | semidirect |
| 33. C2×Q8×C53 | C2×C4 | semidirect |
| 53. #11719924 | C2×C4 | direct (N × H) |
| 58. C2×#88322 | C2×C4 | semidirect |
| 68. Q8×C53 | C22×C4 | semidirect |
| 74. C2×C4×C53 | SD16 | semidirect |
| 88. #88322 | C22×C4 | semidirect |
| 101. C4×C53 | C2×SD16 | semidirect |
| 106. C2×C53 | C4×SD16 | semidirect |
| 112. C2×C4×Q8 | D53 | semidirect |
| 119. C53 | C2×C4×SD16 | semidirect |
| 128. C4×Q8 | C2×D53 | semidirect |
| 144. C2×Q8 | C4×D53 | semidirect |
| 179. Q8 | C2×C4×D53 | semidirect |
| 191. C2×C4 | #11719924 | direct (N × H) |
| 213. C4 | C2×#11719924 | direct (N × H) |
| 217. C2 | C4×#11719924 | direct (N × H) |