Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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×#2162 | C2 | semidirect |
| 3. #11727486 | C2 | semidirect |
| 4. #11725310 | C2 | semidirect |
| 17. C4×C7×C16 | C22 | semidirect |
| 18. #89253 | C22 | semidirect |
| 48. #2162 | D7 | semidirect |
| 94. C4×C16 | C2×D7 | semidirect |
| 229. C7 | #11661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D56 | 2 |
| C7×#2162 | 2 |
| #11727486 | 2 |
| #11725310 | 2 |
| #11661 | 7 |