Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 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. C4×#11719936 | C2 | semidirect |
| 3. C42×#6157 | C2 | semidirect |
| 4. #16811493 | C2 | semidirect |
| 10. #13133282 | C4 | direct (N × H) |
| 14. Q8×Dic53 | C4 | semidirect |
| 16. C4×D212 | C4 | semidirect |
| 18. #13133179 | C4 | semidirect |
| 23. C4×Q8×C53 | C4 | semidirect |
| 40. C4×#6157 | C2×C4 | semidirect |
| 42. #11719936 | C2×C4 | semidirect |
| 63. Q8×C53 | C42 | semidirect |
| 75. D212 | C42 | semidirect |
| 95. C4×C53 | #104 | semidirect |
| 100. Dic53 | #104 | semidirect |
| 113. C53 | C4×#104 | semidirect |
| 117. C4×Q8 | #6157 | semidirect |
| 168. Q8 | C4×#6157 | semidirect |
| 207. C4 | #13133282 | direct (N × H) |