Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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. D53⋊M32 | C2 | semidirect |
| 2. C2×#13133286 | C2 | semidirect |
| 3. #16811536 | C2 | semidirect |
| 4. #16811535 | C2 | semidirect |
| 13. #13133240 | C4 | semidirect |
| 14. #13133239 | C4 | semidirect |
| 17. #13133236 | C4 | semidirect |
| 22. #135×C53 | C4 | semidirect |
| 37. Q16×C53 | C2×C4 | semidirect |
| 39. D8×C53 | C2×C4 | semidirect |
| 46. Dic212 | C2×C4 | semidirect |
| 47. D424 | C2×C4 | semidirect |
| 112. C53 | #2139 | semidirect |
| 119. #135 | #6157 | semidirect |
| 144. Q16 | C2×#6157 | semidirect |
| 151. D8 | C2×#6157 | semidirect |