Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
264 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 92 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. #16811639 | C2 | semidirect |
| 2. C2×C4⋊#88324 | C2 | semidirect |
| 3. Q8⋊#88324 | C2 | semidirect |
| 4. D4⋊#88324 | C2 | semidirect |
| 24. #41×C53 | C8 | semidirect |
| 54. Q8×C53 | C2×C8 | semidirect |
| 57. D4×C53 | C2×C8 | semidirect |
| 107. C53 | #1477 | semidirect |
| 126. #41 | #88324 | semidirect |
| 156. Q8 | C2×#88324 | semidirect |
| 159. D4 | C2×#88324 | semidirect |