Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
332 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. #16810680 | C2 | semidirect |
| 3. #16810366 | C2 | semidirect |
| 4. C53×#432 | C2 | semidirect |
| 12. C4⋊#88322 | C22 | semidirect |
| 16. C4⋊C8×C53 | C22 | semidirect |
| 82. #432 | D53 | semidirect |
| 84. C53 | #1555 | semidirect |
| 94. C4⋊C8 | C2×D53 | semidirect |