Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
322 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 264. C7 | #10604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1546 | 2 |
| #11729543 | 2 |
| C2×#89342 | 2 |
| #11728504 | 2 |
| #11728500 | 2 |
| #11728274 | 2 |
| #11725517 | 2 |
| #10604 | 7 |