Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
562 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 89 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×#89806 | C2 | semidirect |
| 3. C2×#89805 | C2 | semidirect |
| 4. #11729430 | C2 | semidirect |
| 5. #11729430 | C2 | semidirect |
| 6. #11727727 | C2 | semidirect |
| 7. #11725494 | C2 | semidirect |
| 370. C7 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3192 | 2 |
| C2×#89806 | 2 |
| C2×#89805 | 2 |
| #11729430 | 2 |
| #11727727 | 2 |
| #11725494 | 2 |
| #9992 | 7 |