Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 4. #11725437 | C2 | semidirect |
| 5. #11725426 | C2 | semidirect |
| 243. C7 | #8765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2349 | 2 |
| #11729371 | 2 |
| #11729355 | 2 |
| #11725437 | 2 |
| #11725426 | 2 |
| #8765 | 7 |