Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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. #16811529 | C2 | direct (N × H) |
| 9. #13133206 | C4 | semidirect |
| 12. C2×C4×Dic53 | C4 | semidirect |
| 13. C22×Q8×C53 | C4 | semidirect |
| 19. C2×Q8×C53 | C2×C4 | semidirect |
| 33. C4×Dic53 | C2×C4 | semidirect |
| 74. C2×C53 | #354 | semidirect |
| 81. C53 | C2×#354 | semidirect |
| 82. C22×Q8 | #6157 | semidirect |
| 96. C2×Q8 | C2×#6157 | semidirect |
| 153. C2 | #16811529 | direct (N × H) |