Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 4. #11725612 | C2 | semidirect |
| 11. C2×#6392 | C4 | semidirect |
| 196. C7 | #12866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6392 | 2 |
| C2×C7×C22⋊C16 | 2 |
| #11729725 | 2 |
| #11725612 | 2 |
| #12866 | 7 |