Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
456 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×C22⋊#88322 | C2 | semidirect |
| 2. #16810347 | C2 | direct (N × H) |
| 6. C22⋊#88322 | C22 | semidirect |
| 19. C24×C53 | C8 | semidirect |
| 52. C23×C53 | C2×C8 | semidirect |
| 94. C2×C53 | #323 | semidirect |
| 101. C53 | C2×#323 | semidirect |
| 117. C24 | #88322 | semidirect |
| 148. C23 | C2×#88322 | semidirect |
| 191. C2 | #16810347 | direct (N × H) |