Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
348 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. #22626302 | C2 | semidirect |
| 2. #22625151 | C2 | semidirect |
| 3. #22624896 | C2 | semidirect |
| 4. #22624895 | C2 | semidirect |
| 5. #22624894 | C2 | semidirect |
| 6. #22624893 | C2 | semidirect |
| 9. #17989509 | C22 | semidirect |
| 10. #17989509 | C22 | semidirect |
| 14. #17989428 | C22 | semidirect |
| 15. C8×#10596833 | C22 | semidirect |
| 173. C73 | #11670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626302 | 2 |
| #22625151 | 2 |
| #22624896 | 2 |
| #22624895 | 2 |
| #22624894 | 2 |
| #22624893 | 2 |
| #22618839 | 2 |
| #11670 | 73 |