Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13133250 | C2 | semidirect |
| 2. C2×#13133247 | C2 | semidirect |
| 4. C2×#13133145 | C2 | semidirect |
| 5. #16810529 | C2 | semidirect |
| 6. #16810391 | C2 | semidirect |
| 7. C2×#104×C53 | C2 | semidirect |
| 57. C2×Dic106 | D4 | semidirect |
| 59. M16×C53 | D4 | semidirect |
| 71. #11719917 | D4 | semidirect |
| 149. C2×#104 | D53 | semidirect |
| 152. C53 | #2007 | semidirect |
| 210. M16 | C22⋊D53 | semidirect |