Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
960 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 247 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×#89896 | C2 | semidirect |
| 3. C2×C7×#338 | C2 | semidirect |
| 4. #11726477 | C2 | semidirect |
| 5. #11726476 | C2 | semidirect |
| 48. C2×#338 | D7 | semidirect |
| 232. C7 | #23622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89904 | 2 |
| C2×#89896 | 2 |
| C2×C7×#338 | 2 |
| #11726477 | 2 |
| #11726476 | 2 |
| #23622 | 7 |