Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
296 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 236. C7 | #13473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1953 | 2 |
| C2×#89291 | 2 |
| #11728437 | 2 |
| #11727658 | 2 |
| #11727639 | 2 |
| #11725537 | 2 |
| #13473 | 7 |