Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
| 3. C2×#13133217 | C2 | semidirect |
| 4. #16811017 | C2 | semidirect |
| 5. #16811003 | C2 | semidirect |
| 6. #16810996 | C2 | semidirect |
| 7. C4×M16×C53 | C2 | semidirect |
| 38. M16×C53 | D4 | semidirect |
| 75. C4×C53 | #137 | semidirect |
| 90. C4×M16 | D53 | semidirect |
| 91. C53 | #3152 | semidirect |
| 124. M16 | D212 | semidirect |
| 161. C4 | #13133250 | semidirect |