Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3246 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 3246 conjugacy classes of subgroups — too many to draw. Only its 491 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. #11729881 | C2 | semidirect |
| 4. #11729302 | C2 | semidirect |
| 8. C22×C7×C22⋊C4 | C4 | semidirect |
| 13. C2×C7⋊#95 | C22 | semidirect |
| 70. C22×C22⋊C4 | Dic7 | semidirect |
| 199. C7 | #14341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×C22⋊C4 | 2 |
| C2×#90019 | 2 |
| #11729881 | 2 |
| #11729302 | 2 |
| #14341 | 7 |