Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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×C7×#349 | C2 | semidirect |
| 3. #11729742 | C2 | semidirect |
| 4. C2×#89313 | C2 | semidirect |
| 5. #11729193 | C2 | semidirect |
| 6. #11729182 | C2 | semidirect |
| 7. #11725625 | C2 | semidirect |
| 62. C7×M32 | D4 | semidirect |
| 81. C2×#349 | D7 | semidirect |
| 238. M32 | C22⋊D7 | semidirect |
| 384. C7 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11741216 | 2 |
| C2×C7×#349 | 2 |
| #11729742 | 2 |
| C2×#89313 | 2 |
| #11729193 | 2 |
| #11729182 | 2 |
| #11725625 | 2 |
| #13386 | 7 |