Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 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. C7×#2140 | C2 | semidirect |
| 3. C2×#89358 | C2 | semidirect |
| 4. C2×#89311 | C2 | semidirect |
| 5. #11728416 | C2 | semidirect |
| 6. #11728406 | C2 | semidirect |
| 7. #11725616 | C2 | semidirect |
| 54. C7×#107 | D4 | semidirect |
| 68. #2140 | D7 | semidirect |
| 200. #107 | C22⋊D7 | semidirect |
| 308. C7 | #13413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89923 | 2 |
| C7×#2140 | 2 |
| C2×#89358 | 2 |
| C2×#89311 | 2 |
| #11728416 | 2 |
| #11728406 | 2 |
| #11725616 | 2 |
| #13413 | 7 |