Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
800 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 289 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. #16811098 | C2 | semidirect |
| 2. #16810597 | C2 | semidirect |
| 3. C2×#13133132 | C2 | semidirect |
| 6. #13133176 | C22 | semidirect |
| 7. C2×C22⋊Dic53 | C22 | semidirect |
| 8. #13133132 | C22 | semidirect |
| 10. C2×#41×C53 | C4 | semidirect |
| 12. C22×D4×C53 | C4 | semidirect |
| 15. C24×C53 | C2×C4 | semidirect |
| 19. C2×Q8×C53 | C2×C4 | semidirect |
| 23. C2×D4×C53 | C2×C4 | semidirect |
| 24. C2×D4×C53 | C2×C4 | semidirect |
| 27. C22×C4×C53 | C2×C4 | semidirect |
| 28. C22×C4×C53 | C2×C4 | semidirect |
| 76. C53 | #2883 | semidirect |
| 78. C2×#41 | Dic53 | semidirect |
| 80. C22×D4 | Dic53 | semidirect |
| 87. C24 | C2×Dic53 | semidirect |
| 91. C2×Q8 | C2×Dic53 | semidirect |
| 95. C2×D4 | C2×Dic53 | semidirect |
| 96. C2×D4 | C2×Dic53 | semidirect |
| 100. C22×C4 | C2×Dic53 | semidirect |
| 101. C22×C4 | C2×Dic53 | semidirect |