Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
436 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 149 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. #16810985 | C2 | direct (N × H) |
| 3. C2×#13133140 | C2 | semidirect |
| 5. C2×#13133128 | C2 | semidirect |
| 6. C2×C4⋊Q8×C53 | C2 | semidirect |
| 14. #13133140 | C22 | semidirect |
| 16. #13133128 | C22 | semidirect |
| 19. C4⋊Q8×C53 | C22 | semidirect |
| 83. C2×C53 | #489 | semidirect |
| 88. C2×C4⋊Q8 | D53 | semidirect |
| 94. C53 | C2×#489 | semidirect |
| 100. C4⋊Q8 | C2×D53 | semidirect |
| 171. C2 | #16810985 | direct (N × H) |