Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
690 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 127 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. #11729626 | C2 | semidirect |
| 3. C2×#89337 | C2 | semidirect |
| 4. #11729413 | C2 | semidirect |
| 314. C7 | #12729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3510 | 2 |
| #11729626 | 2 |
| C2×#89337 | 2 |
| #11729413 | 2 |
| #12729 | 7 |