Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#11719924 | C2 | semidirect |
| 3. #16810823 | C2 | direct (N × H) |
| 4. C2×C4⋊#88322 | C2 | semidirect |
| 5. C2×#13133137 | C2 | semidirect |
| 6. C2×C4×Q8×C53 | C2 | semidirect |
| 11. C2×#11719924 | C22 | semidirect |
| 15. C4⋊#88322 | C22 | semidirect |
| 16. #13133137 | C22 | semidirect |
| 19. C4×Q8×C53 | C22 | semidirect |
| 27. C2×Q8×C53 | D4 | semidirect |
| 58. Q8×C53 | C2×D4 | semidirect |
| 64. C2×C4×C53 | SD16 | semidirect |
| 89. C4×C53 | C2×SD16 | semidirect |
| 93. C2×C53 | #460 | semidirect |
| 100. C2×C4×Q8 | D53 | semidirect |
| 104. C53 | C2×#460 | semidirect |
| 115. C4×Q8 | C2×D53 | semidirect |
| 125. C2×Q8 | D212 | semidirect |
| 156. Q8 | C2×D212 | semidirect |
| 167. C2×C4 | #11719924 | semidirect |
| 187. C4 | C2×#11719924 | semidirect |
| 191. C2 | #16810823 | direct (N × H) |