Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 221 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. C2×#13133136 | C2 | semidirect |
| 4. C2×#13133135 | C2 | semidirect |
| 5. #101×D53 | C2 | direct (N × H) |
| 6. C2×#101×C53 | C2 | semidirect |
| 21. #13133136 | C22 | semidirect |
| 22. #13133135 | C22 | semidirect |
| 25. #101×C53 | C22 | semidirect |
| 102. C2×D53 | #101 | direct (N × H) |
| 113. C2×C53 | C2×#101 | semidirect |
| 116. D53 | C2×#101 | direct (N × H) |
| 122. C2×#101 | D53 | direct (N × H) |
| 123. C53 | C22×#101 | semidirect |
| 142. #101 | C2×D53 | direct (N × H) |
| 231. C2 | #101×D53 | direct (N × H) |