Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#13133248 | C2 | semidirect |
| 3. #16811015 | C2 | semidirect |
| 4. #16811002 | C2 | semidirect |
| 5. #16810997 | C2 | semidirect |
| 6. C4×#11719917 | C2 | semidirect |
| 7. C2×C4⋊Q8×C53 | C2 | semidirect |
| 47. #11719917 | D4 | semidirect |
| 76. C4×C53 | #137 | semidirect |
| 86. C2×C4⋊Q8 | D53 | semidirect |
| 91. C53 | #3152 | semidirect |
| 161. C4 | #13133248 | semidirect |