Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
432 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 246. C7 | #9456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2568 | 2 |
| #11739881 | 2 |
| #11729530 | 2 |
| #11729379 | 2 |
| #11725427 | 2 |
| #9456 | 7 |