Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#13133144 | C2 | semidirect |
| 3. #16810627 | C2 | semidirect |
| 4. #16810524 | C2 | semidirect |
| 5. #16810392 | C2 | semidirect |
| 6. #16810382 | C2 | semidirect |
| 7. C53×#520 | C2 | semidirect |
| 10. #13133242 | C4 | semidirect |
| 46. C2×D212 | C2×C4 | semidirect |
| 64. #11719917 | C2×C4 | semidirect |
| 75. Q8×C53 | C22⋊C4 | semidirect |
| 79. D4×C53 | C22⋊C4 | semidirect |
| 134. #520 | D53 | semidirect |
| 140. C53 | #1883 | semidirect |
| 208. Q8 | #11719921 | semidirect |
| 216. D4 | #11719921 | semidirect |