Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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×#89312 | C2 | semidirect |
| 3. #11729199 | C2 | semidirect |
| 6. #11727548 | C2 | semidirect |
| 7. C7×#1376 | C2 | semidirect |
| 70. #1376 | D7 | semidirect |
| 298. C7 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89468 | 2 |
| C2×#89312 | 2 |
| #11729199 | 2 |
| C2×#89311 | 2 |
| #11729194 | 2 |
| #11727548 | 2 |
| C7×#1376 | 2 |
| #13414 | 7 |