Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #16810493 | C2 | semidirect |
| 4. #16810386 | C2 | semidirect |
| 5. C2×C4⋊C8×C53 | C2 | semidirect |
| 9. C4×D212 | C4 | semidirect |
| 75. D212 | C4⋊C4 | semidirect |
| 93. C4×C53 | #102 | semidirect |
| 110. C2×C4⋊C8 | D53 | semidirect |
| 114. C53 | #1802 | semidirect |
| 204. C4 | #13133139 | semidirect |