Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 165. C7 | #13458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89455 | 2 |
| C2×#89308 | 2 |
| #11727548 | 2 |
| C7×#1376 | 2 |
| #11725625 | 2 |
| #13458 | 7 |