Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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. #16811626 | C2 | semidirect |
| 2. C4×#11719940 | C2 | semidirect |
| 3. Q8⋊#88324 | C2 | semidirect |
| 4. D4⋊#88324 | C2 | semidirect |
| 55. Q8×C53 | M16 | semidirect |
| 58. D4×C53 | M16 | semidirect |
| 108. C53 | #1489 | semidirect |
| 158. Q8 | #11719940 | semidirect |
| 161. D4 | #11719940 | semidirect |