Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #16810895 | C2 | direct (N × H) |
| 4. C2×#13133153 | C2 | semidirect |
| 5. C2×#13133136 | C2 | semidirect |
| 6. C22×Q16×C53 | C2 | semidirect |
| 18. #13133153 | C22 | semidirect |
| 19. #13133136 | C22 | semidirect |
| 24. C2×Q16×C53 | C22 | semidirect |
| 101. C2×C53 | #473 | semidirect |
| 105. C22×Q16 | D53 | semidirect |
| 110. C53 | C2×#473 | semidirect |
| 119. C2×Q16 | C2×D53 | semidirect |
| 205. C2 | #16810895 | direct (N × H) |