Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
552 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 186 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×#11719936 | C2 | semidirect |
| 2. C22×#11719940 | C2 | semidirect |
| 3. #16811656 | C2 | direct (N × H) |
| 4. C2×#13133284 | C2 | semidirect |
| 5. C2×#13133274 | C2 | semidirect |
| 6. C2×C22⋊#88324 | C2 | semidirect |
| 7. C2×C4×#88324 | C2 | semidirect |
| 10. C2×#11719936 | C22 | semidirect |
| 12. C2×#11719940 | C22 | semidirect |
| 17. #13133284 | C22 | semidirect |
| 18. #13133274 | C22 | semidirect |
| 19. C22⋊#88324 | C22 | semidirect |
| 20. C4×#88324 | C22 | semidirect |
| 51. C2×#88324 | D4 | semidirect |
| 80. C2×Dic53 | M16 | semidirect |
| 93. #88324 | C2×D4 | semidirect |
| 110. Dic53 | C2×M16 | semidirect |
| 115. C2×C53 | #436 | semidirect |
| 128. C53 | C2×#436 | semidirect |
| 235. C2 | #16811656 | direct (N × H) |