Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 32. Dic56 | Q8 | semidirect |
| 138. C7 | #13706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11727074 | 2 |
| #11727072 | 2 |
| C7×#1423 | 2 |
| #11725403 | 2 |
| Dic7⋊C32 | 2 |
| #11725384 | 2 |
| #11725381 | 2 |
| #13706 | 7 |