Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13133191 | C2 | semidirect |
| 2. #16810937 | C2 | semidirect |
| 3. #16810859 | C2 | semidirect |
| 4. #16810759 | C2 | semidirect |
| 5. C2×C22⋊C8×C53 | C2 | semidirect |
| 6. C22×D212 | C22 | semidirect |
| 8. C2×D424 | C22 | semidirect |
| 12. #13133191 | C22 | semidirect |
| 13. C2×C4⋊Dic53 | C22 | semidirect |
| 15. #13133151 | C22 | semidirect |
| 16. #13133139 | C22 | semidirect |
| 18. C22×C8×C53 | C22 | semidirect |
| 19. C22⋊C8×C53 | C22 | semidirect |
| 43. C23×C53 | D8 | semidirect |
| 91. C2×C22⋊C8 | D53 | semidirect |
| 92. C53 | #3186 | semidirect |
| 97. C22×C8 | C2×D53 | semidirect |
| 106. C22⋊C8 | C2×D53 | semidirect |
| 134. C23 | D424 | semidirect |