Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
344 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4⋊#88322 | C2 | semidirect |
| 2. C2×C4×#88322 | C2 | semidirect |
| 3. D4⋊#88322 | C2 | direct (N × H) |
| 8. C4⋊#88322 | C22 | semidirect |
| 10. C4×#88322 | C22 | semidirect |
| 23. C2×D4×C53 | C8 | semidirect |
| 52. D4×C53 | C2×C8 | semidirect |
| 90. C2×C53 | D4⋊C8 | semidirect |
| 98. C53 | C2×D4⋊C8 | semidirect |
| 117. C2×D4 | #88322 | semidirect |
| 146. D4 | C2×#88322 | semidirect |
| 183. C2 | D4⋊#88322 | direct (N × H) |