Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
514 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #11729528 | C2 | semidirect |
| 5. #11725426 | C2 | semidirect |
| 238. C7 | #9399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2563 | 2 |
| #11739749 | 2 |
| #11729528 | 2 |
| #11729371 | 2 |
| #11725426 | 2 |
| #9399 | 7 |