Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1154 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#89320 | C2 | semidirect |
| 3. #11729285 | C2 | semidirect |
| 228. C7 | #8305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#124 | 2 |
| C2×#89320 | 2 |
| #11729285 | 2 |
| #8305 | 7 |