Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#13133248 | C2 | semidirect |
| 3. C2×#13133144 | C2 | semidirect |
| 4. C2×#13133143 | C2 | semidirect |
| 5. #16810530 | C2 | semidirect |
| 6. #16810391 | C2 | semidirect |
| 7. C2×#137×C53 | C2 | semidirect |
| 41. C2×Q8×C53 | D4 | semidirect |
| 61. M16×C53 | D4 | semidirect |
| 73. #11719917 | D4 | semidirect |
| 146. C2×#137 | D53 | semidirect |
| 152. C53 | #2007 | semidirect |
| 191. C2×Q8 | C22⋊D53 | semidirect |
| 210. M16 | C22⋊D53 | semidirect |