Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1518 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1518 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 2. #11729880 | C2 | semidirect |
| 3. C2×#89320 | C2 | semidirect |
| 264. C7 | #8307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#121 | 2 |
| #11729880 | 2 |
| C2×#89320 | 2 |
| #8307 | 7 |