Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 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 |
|---|---|---|
| 2. #16810645 | C2 | semidirect |
| 3. C4×#11719912 | C2 | semidirect |
| 4. Q8⋊#88322 | C2 | semidirect |
| 5. #16810352 | C2 | semidirect |
| 6. #16810350 | C2 | semidirect |
| 7. C53×Q8⋊C8 | C2 | semidirect |
| 61. Q8×C53 | M16 | semidirect |
| 73. D212 | M16 | semidirect |
| 115. Q8⋊C8 | D53 | semidirect |
| 118. C53 | #1489 | semidirect |
| 172. Q8 | #11719912 | semidirect |