Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
480 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 170 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. #16811663 | C2 | direct (N × H) |
| 18. C2×Dic212 | C4 | semidirect |
| 19. C2×#11719925 | C4 | semidirect |
| 20. Q16×D53 | C4 | semidirect |
| 23. C2×Q16×C53 | C4 | semidirect |
| 44. Q16×C53 | C2×C4 | semidirect |
| 46. #11719925 | C2×C4 | semidirect |
| 48. Dic212 | C2×C4 | semidirect |
| 88. C2×C53 | #441 | semidirect |
| 90. D53 | #441 | semidirect |
| 98. C53 | C2×#441 | semidirect |
| 104. C2×Q16 | #6157 | semidirect |
| 129. Q16 | C2×#6157 | semidirect |
| 181. C2 | #16811663 | direct (N × H) |