Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. C2×#13133236 | C2 | semidirect |
| 2. #16811052 | C2 | direct (N × H) |
| 3. C2×Dic424 | C2 | semidirect |
| 4. C2×#13133161 | C2 | semidirect |
| 5. C2×C16×D53 | C2 | semidirect |
| 6. C2×D16×C53 | C2 | semidirect |
| 9. #13133236 | C22 | semidirect |
| 13. Dic424 | C22 | semidirect |
| 14. #13133161 | C22 | semidirect |
| 16. C16×D53 | C22 | semidirect |
| 18. D16×C53 | C22 | semidirect |
| 65. C2×C53 | #508 | semidirect |
| 72. C2×D16 | D53 | semidirect |
| 74. C53 | C2×#508 | semidirect |
| 84. D16 | C2×D53 | semidirect |
| 133. C2 | #16811052 | direct (N × H) |