Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
448 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #22611625 | C2 | semidirect |
| 3. #22611586 | C2 | semidirect |
| 5. #22609979 | C2 | semidirect |
| 6. #22609734 | C2 | semidirect |
| 8. C22×#11924016 | C4 | semidirect |
| 16. #17988623 | C4 | semidirect |
| 17. #17988595 | C4 | semidirect |
| 18. #17988592 | C4 | semidirect |
| 218. C73 | #13232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22619567 | 2 |
| #22611625 | 2 |
| #22611586 | 2 |
| #22611581 | 2 |
| #22609979 | 2 |
| #22609734 | 2 |
| C73×#2134 | 2 |
| #13232 | 73 |