Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
180 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 148. C7 | #7091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11728216 | 2 |
| C7×#1292 | 2 |
| #11725515 | 2 |
| #7091 | 7 |