Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22620676 | C2 | semidirect |
| 2. #22620672 | C2 | semidirect |
| 4. #22609593 | C2 | semidirect |
| 5. #22609592 | C2 | semidirect |
| 6. #22609590 | C2 | semidirect |
| 7. #22609542 | C2 | semidirect |
| 8. #22608234 | C2 | semidirect |
| 11. #17988985 | C22 | semidirect |
| 12. #17988983 | C22 | semidirect |
| 13. #17988967 | C22 | semidirect |
| 14. #17988966 | C22 | semidirect |
| 16. #17988939 | C22 | semidirect |
| 17. #17988938 | C22 | semidirect |
| 18. #17988937 | C22 | semidirect |
| 29. #17988309 | C22 | semidirect |
| 30. #17988308 | C22 | semidirect |
| 31. C8×#10596831 | C22 | semidirect |
| 169. C73 | #19753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620676 | 2 |
| #22620672 | 2 |
| #22620305 | 2 |
| #22609593 | 2 |
| #22609592 | 2 |
| #22609590 | 2 |
| #22609542 | 2 |
| #22608234 | 2 |
| C73×#3138 | 2 |
| #19753 | 73 |