Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
498 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11725423 | C2 | semidirect |
| 162. C7 | #8736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2312 | 2 |
| C2×#89320 | 2 |
| #11725423 | 2 |
| #8736 | 7 |