Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#13133137 | C2 | semidirect |
| 3. C2×#13133137 | C2 | semidirect |
| 4. #16810378 | C2 | semidirect |
| 5. C53×#389 | C2 | semidirect |
| 39. C4⋊C4×C53 | D4 | semidirect |
| 107. #389 | D53 | semidirect |
| 109. C53 | #2041 | semidirect |
| 146. C4⋊C4 | D212 | semidirect |