Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 191. C7 | #10623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1984 | 2 |
| #11729380 | 2 |
| #11727516 | 2 |
| #11725508 | 2 |
| #11725460 | 2 |
| #10623 | 7 |