Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
376 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 78 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×#13133285 | C2 | semidirect |
| 2. C2×#13133279 | C2 | semidirect |
| 3. C2×#13133271 | C2 | semidirect |
| 4. #16811575 | C2 | semidirect |
| 14. C2×D424 | C4 | semidirect |
| 15. C2×#11719922 | C4 | semidirect |
| 19. C2×D8×C53 | C4 | semidirect |
| 70. C8×C53 | C22⋊C4 | semidirect |
| 71. #88322 | C22⋊C4 | semidirect |
| 101. C53 | #1972 | semidirect |
| 107. C2×D8 | #6157 | semidirect |
| 167. C8 | C22⋊#6157 | semidirect |