Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22608482 | C2 | semidirect |
| 5. #22607804 | C2 | semidirect |
| 6. #22607797 | C2 | semidirect |
| 7. C73×#2987 | C2 | semidirect |
| 9. #17988990 | C4 | semidirect |
| 10. #17988961 | C4 | semidirect |
| 11. #17988937 | C4 | semidirect |
| 12. #17988935 | C4 | semidirect |
| 157. #2987 | D73 | semidirect |
| 163. C73 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620650 | 2 |
| #22608565 | 2 |
| #22608482 | 2 |
| #22608479 | 2 |
| #22607804 | 2 |
| #22607797 | 2 |
| C73×#2987 | 2 |
| #9418 | 73 |