Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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. D53⋊#108 | C2 | semidirect |
| 2. C2×#13133285 | C2 | semidirect |
| 4. #16811502 | C2 | semidirect |
| 16. #13133225 | C4 | semidirect |
| 17. #13133224 | C4 | semidirect |
| 19. #13133223 | C4 | semidirect |
| 24. #131×C53 | C4 | semidirect |
| 118. C53 | #1815 | semidirect |
| 125. #131 | #6157 | semidirect |