Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 178 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. Q16×#6157 | 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 |
| 45. Q16×C53 | C2×C4 | semidirect |
| 47. #11719925 | C2×C4 | semidirect |
| 49. Dic212 | C2×C4 | semidirect |
| 56. C2×#6157 | Q16 | direct (N × H) |
| 85. #6157 | C2×Q16 | direct (N × H) |
| 93. C2×C53 | C4×Q16 | semidirect |
| 95. D53 | C4×Q16 | semidirect |
| 104. C53 | C2×C4×Q16 | semidirect |
| 110. C2×Q16 | #6157 | direct (N × H) |
| 136. Q16 | C2×#6157 | direct (N × H) |
| 193. C2 | Q16×#6157 | direct (N × H) |