Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 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. C4×C4⋊Dic53 | C2 | semidirect |
| 4. #16810386 | C2 | semidirect |
| 5. C2×C4×C8×C53 | C2 | semidirect |
| 9. C4×D212 | C4 | semidirect |
| 14. #13133139 | C4 | direct (N × H) |
| 34. C2×C8×C53 | C2×C4 | semidirect |
| 41. C4⋊Dic53 | C2×C4 | semidirect |
| 66. D212 | C42 | semidirect |
| 80. C4×C53 | #102 | semidirect |
| 95. C2×C4×C8 | D53 | semidirect |
| 98. C53 | C4×#102 | semidirect |
| 127. C2×C8 | C4×D53 | semidirect |
| 175. C4 | #13133139 | direct (N × H) |