Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
406 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 2. C7×#2110 | C2 | semidirect |
| 3. C2×#89310 | C2 | semidirect |
| 4. #11729189 | C2 | semidirect |
| 5. #11727636 | C2 | semidirect |
| 50. #2110 | D7 | semidirect |
| 208. C7 | #13199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736024 | 2 |
| C7×#2110 | 2 |
| C2×#89310 | 2 |
| #11729189 | 2 |
| #11727636 | 2 |
| #13199 | 7 |