Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 223. C7 | #10664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1570 | 2 |
| #11728524 | 2 |
| #11728271 | 2 |
| #11728254 | 2 |
| #11728227 | 2 |
| #11728176 | 2 |
| #11725546 | 2 |
| #10664 | 7 |