Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
182 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 73 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. #16810701 | C2 | semidirect |
| 2. D4×#88322 | C2 | semidirect |
| 3. #16810376 | C2 | semidirect |
| 4. D4⋊#88322 | C2 | semidirect |
| 5. D4⋊#88322 | C2 | semidirect |
| 6. #16810345 | C2 | semidirect |
| 47. D4×C53 | M16 | semidirect |
| 63. #88322 | D8 | semidirect |
| 91. C53 | #1581 | semidirect |
| 131. D4 | #11719917 | semidirect |