Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 139 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. #16810997 | C2 | semidirect |
| 3. #16810825 | C2 | semidirect |
| 4. #16810823 | C2 | semidirect |
| 5. Q8×#88322 | C2 | semidirect |
| 6. C4×#11719924 | C2 | semidirect |
| 7. C53×#557 | C2 | semidirect |
| 47. Q8×C53 | SD16 | semidirect |
| 60. #88322 | #41 | semidirect |
| 77. #557 | D53 | semidirect |
| 84. C53 | #3392 | semidirect |
| 124. Q8 | #11719924 | semidirect |