Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. D53⋊#131 | C2 | semidirect |
| 2. #16811692 | C2 | semidirect |
| 3. #16811616 | C2 | semidirect |
| 4. #16811614 | C2 | semidirect |
| 5. #16811613 | C2 | semidirect |
| 6. C2×#13133280 | C2 | semidirect |
| 22. #13133265 | C4 | semidirect |
| 24. #13133264 | C4 | semidirect |
| 25. #13133264 | C4 | semidirect |
| 31. 2−1+4×C53 | C4 | semidirect |
| 35. #41×C53 | C2×C4 | semidirect |
| 37. C2×Q8×C53 | C2×C4 | semidirect |
| 39. #11719949 | C2×C4 | semidirect |
| 45. Q8×D53 | C2×C4 | semidirect |
| 51. #11719947 | C2×C4 | semidirect |
| 60. #11719945 | C2×C4 | semidirect |
| 66. C2×Dic106 | C2×C4 | semidirect |
| 149. C53 | #2898 | semidirect |
| 155. 2−1+4 | #6157 | semidirect |
| 189. #41 | C2×#6157 | semidirect |
| 201. C2×Q8 | C2×#6157 | semidirect |