Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 394 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×#13133247 | C2 | semidirect |
| 3. C2×#13133205 | C2 | semidirect |
| 4. #16810633 | C2 | semidirect |
| 5. C2×#13133133 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 7. C2×#104×C53 | C2 | semidirect |
| 53. C2×Dic106 | D4 | semidirect |
| 58. C42×C53 | D4 | semidirect |
| 67. #11719917 | D4 | semidirect |
| 135. C2×#104 | D53 | semidirect |
| 139. C53 | #2004 | semidirect |
| 200. C42 | C22⋊D53 | semidirect |