Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4⋊#88322 | C2 | semidirect |
| 3. #16810352 | C2 | direct (N × H) |
| 4. C2×C4×C8×C53 | C2 | semidirect |
| 15. C4⋊#88322 | C22 | semidirect |
| 19. C4×C8×C53 | C22 | semidirect |
| 27. C2×D212 | C8 | semidirect |
| 65. D212 | C2×C8 | semidirect |
| 89. C2×C53 | D4⋊C8 | semidirect |
| 96. C2×C4×C8 | D53 | semidirect |
| 98. C53 | C2×D4⋊C8 | semidirect |
| 113. C4×C8 | C2×D53 | semidirect |
| 183. C2 | #16810352 | direct (N × H) |