Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×D424 | C2 | semidirect |
| 2. C2×#13133191 | C2 | semidirect |
| 3. C2×#13133139 | C2 | semidirect |
| 4. #16810386 | C2 | semidirect |
| 5. C2×C22⋊C8×C53 | C2 | semidirect |
| 36. C2×D212 | D4 | semidirect |
| 40. C2×C8×C53 | D4 | semidirect |
| 43. C4⋊Dic53 | D4 | semidirect |
| 49. C23×C53 | D8 | semidirect |
| 110. C2×C22⋊C8 | D53 | semidirect |
| 112. C53 | #1999 | semidirect |
| 148. C2×C8 | C22⋊D53 | semidirect |
| 163. C23 | D424 | semidirect |