Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
326 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 15. C7×#347 | C4 | semidirect |
| 16. #89261 | C4 | semidirect |
| 80. #347 | Dic7 | semidirect |
| 179. C7 | #12595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#347 | 2 |
| Dic7×#97 | 2 |
| C2×#89261 | 2 |
| #11725618 | 2 |
| #11725616 | 2 |
| #12595 | 7 |