Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
622 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11740759 | C2 | semidirect |
| 3. #11739820 | C2 | semidirect |
| 4. #11729568 | C2 | semidirect |
| 5. #11729352 | C2 | semidirect |
| 6. #11728521 | C2 | semidirect |
| 7. #11725544 | C2 | semidirect |
| 126. C2×Dic14 | D8 | semidirect |
| 451. C7 | #9997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3100 | 2 |
| #11740759 | 2 |
| #11739820 | 2 |
| #11729568 | 2 |
| #11729352 | 2 |
| #11728521 | 2 |
| #11725544 | 2 |
| #9997 | 7 |