Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
482 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 4. #11726823 | C2 | semidirect |
| 26. C2×C7×C16 | Q8 | semidirect |
| 86. C2×C16 | Dic14 | semidirect |
| 133. C7 | #33728 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735887 | 2 |
| C2×C7×#346 | 2 |
| #11729158 | 2 |
| #11726823 | 2 |
| #33728 | 7 |