Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
402 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 80 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×#13133280 | C2 | semidirect |
| 4. (C2×#6157)⋊Q8 | C2 | semidirect |
| 5. #16811497 | C2 | semidirect |
| 6. (C2×#6157)⋊C8 | C2 | semidirect |
| 22. C2×#11719913 | C4 | semidirect |
| 23. C2×#11719923 | C4 | semidirect |
| 24. C2×#11719924 | C4 | semidirect |
| 28. C2×SD16×C53 | C4 | semidirect |
| 37. C2×Q8×C53 | C2×C4 | semidirect |
| 52. C2×Dic106 | C2×C4 | semidirect |
| 64. C2×C8×C53 | C2×C4 | semidirect |
| 67. C2×#88322 | C2×C4 | semidirect |
| 92. C2×#6157 | SD16 | semidirect |
| 162. C53 | #1877 | semidirect |
| 171. C2×SD16 | #6157 | semidirect |
| 191. C2×Q8 | C2×#6157 | semidirect |
| 218. C2×C8 | C2×#6157 | semidirect |