Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q16×D53 | C2 | semidirect |
| 2. C2×#13133161 | C2 | semidirect |
| 4. #16810428 | C2 | semidirect |
| 5. #16810427 | C2 | semidirect |
| 6. #16810402 | C2 | semidirect |
| 7. C2×SD32×C53 | C2 | semidirect |
| 33. Q16×C53 | D4 | semidirect |
| 42. Dic212 | D4 | semidirect |
| 74. C2×D53 | SD32 | semidirect |
| 89. C2×SD32 | D53 | semidirect |
| 94. C53 | #2185 | semidirect |
| 123. Q16 | C22⋊D53 | semidirect |