Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
826 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 826 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 |
|---|---|---|
| 3. #11740187 | C2 | semidirect |
| 5. #11729445 | C2 | semidirect |
| 6. #11727677 | C2 | semidirect |
| 7. #11725486 | C2 | semidirect |
| 411. C7 | #9990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#450 | 2 |
| C2×#89990 | 2 |
| #11740187 | 2 |
| #11729883 | 2 |
| #11729445 | 2 |
| #11727677 | 2 |
| #11725486 | 2 |
| #9990 | 7 |