Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
992 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#11719917 | C2 | semidirect |
| 3. C2×#13133133 | C2 | direct (N × H) |
| 4. C22×M16×C53 | C2 | semidirect |
| 13. C2×#11719917 | C22 | semidirect |
| 15. #13133133 | C22 | direct (N × H) |
| 18. C2×M16×C53 | C22 | semidirect |
| 41. M16×C53 | C23 | semidirect |
| 44. #11719917 | C23 | semidirect |
| 73. C22×C53 | #100 | semidirect |
| 88. C2×C53 | C2×#100 | semidirect |
| 93. C22×M16 | D53 | semidirect |
| 95. C53 | C22×#100 | semidirect |
| 107. C2×M16 | C2×D53 | semidirect |
| 134. M16 | C22×D53 | semidirect |
| 168. C22 | #13133133 | direct (N × H) |
| 179. C2 | C2×#13133133 | direct (N × H) |