Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
406 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 21. #17988309 | C4 | semidirect |
| 22. #17988309 | C4 | semidirect |
| 23. #17988308 | C4 | semidirect |
| 24. #322×C73 | C4 | semidirect |
| 150. C73 | #8821 | semidirect |
| 167. #322 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625867 | 2 |
| #22625866 | 2 |
| #22625852 | 2 |
| #322×D73 | 2 |
| #8821 | 73 |