Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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. #16811031 | C2 | semidirect |
| 4. #16811030 | C2 | semidirect |
| 5. #16811024 | C2 | semidirect |
| 6. #16811023 | C2 | semidirect |
| 50. M16×C53 | Q8 | semidirect |
| 78. #11719917 | Q8 | semidirect |
| 136. C53 | #3166 | semidirect |
| 176. M16 | Dic106 | semidirect |