Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #16810825 | C2 | direct (N × H) |
| 4. C2×C4⋊#88322 | C2 | semidirect |
| 5. C2×#13133141 | C2 | semidirect |
| 6. C2×C4⋊Q8×C53 | C2 | semidirect |
| 16. C4⋊#88322 | C22 | semidirect |
| 17. #13133141 | C22 | semidirect |
| 20. C4⋊Q8×C53 | C22 | semidirect |
| 61. C2×C4×C53 | SD16 | semidirect |
| 86. C4×C53 | C2×SD16 | semidirect |
| 91. C2×C53 | #461 | semidirect |
| 97. C2×C4⋊Q8 | D53 | semidirect |
| 102. C53 | C2×#461 | semidirect |
| 110. C4⋊Q8 | C2×D53 | semidirect |
| 163. C2×C4 | #11719924 | semidirect |
| 183. C4 | C2×#11719924 | semidirect |
| 187. C2 | #16810825 | direct (N × H) |