Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
668 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#11719913 | C2 | semidirect |
| 2. C22×D424 | C2 | semidirect |
| 3. C2×#13133214 | C2 | semidirect |
| 4. C2×#13133205 | C2 | semidirect |
| 5. #16811012 | C2 | direct (N × H) |
| 6. C2×#97×C53 | C2 | semidirect |
| 12. C2×#11719913 | C22 | semidirect |
| 14. C2×D424 | C22 | semidirect |
| 16. #13133214 | C22 | semidirect |
| 18. #13133205 | C22 | semidirect |
| 22. #97×C53 | C22 | semidirect |
| 40. C2×C8×C53 | D4 | semidirect |
| 69. C8×C53 | C2×D4 | semidirect |
| 84. C2×C53 | #496 | semidirect |
| 94. C2×#97 | D53 | semidirect |
| 95. C53 | C2×#496 | semidirect |
| 111. #97 | C2×D53 | semidirect |
| 131. C2×C8 | D212 | semidirect |
| 158. C8 | C2×D212 | semidirect |
| 174. C2 | #16811012 | direct (N × H) |