Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 228. C7 | #8766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2351 | 2 |
| #11729391 | 2 |
| #11729378 | 2 |
| #11725437 | 2 |
| #11725426 | 2 |
| #8766 | 7 |