Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
426 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 141 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. #16811295 | C2 | semidirect |
| 2. #16810971 | C2 | semidirect |
| 3. #16810900 | C2 | semidirect |
| 4. #16810818 | C2 | semidirect |
| 5. Q8×#88322 | C2 | semidirect |
| 6. C4×#11719922 | C2 | semidirect |
| 7. D4×Q8×C53 | C2 | semidirect |
| 47. Q8×C53 | D8 | semidirect |
| 49. D4×C53 | #41 | semidirect |
| 83. D4×Q8 | D53 | semidirect |
| 89. C53 | #3358 | semidirect |
| 129. Q8 | #11719922 | semidirect |
| 135. D4 | #11719949 | semidirect |