Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#13133153 | C2 | semidirect |
| 3. #16810431 | C2 | direct (N × H) |
| 4. C22×C16×C53 | C2 | semidirect |
| 15. #13133153 | C22 | semidirect |
| 19. C2×C16×C53 | C22 | semidirect |
| 81. C2×C53 | #359 | semidirect |
| 85. C22×C16 | D53 | semidirect |
| 88. C53 | C2×#359 | semidirect |
| 101. C2×C16 | C2×D53 | semidirect |
| 165. C2 | #16810431 | direct (N × H) |