Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
874 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 159 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. #22620861 | C2 | semidirect |
| 2. #22620850 | C2 | semidirect |
| 3. #22620670 | C2 | semidirect |
| 4. #22620382 | C2 | semidirect |
| 5. #22609597 | C2 | semidirect |
| 6. #22609595 | C2 | semidirect |
| 7. #22609567 | C2 | semidirect |
| 8. #22609545 | C2 | semidirect |
| 9. #22609533 | C2 | semidirect |
| 10. #22608229 | C2 | semidirect |
| 11. C73×#1715 | C2 | semidirect |
| 18. #17988964 | C22 | semidirect |
| 21. #17988963 | C22 | semidirect |
| 24. #17988937 | C22 | semidirect |
| 26. #17988935 | C22 | semidirect |
| 27. #17988934 | C22 | semidirect |
| 36. #17988308 | C22 | semidirect |
| 37. C8×#10596831 | C22 | semidirect |
| 38. #498×C73 | C22 | semidirect |
| 40. #492×C73 | C22 | semidirect |
| 42. #322×C73 | C22 | semidirect |
| 205. #1715 | D73 | semidirect |
| 209. C73 | #19727 | semidirect |
| 214. #498 | C2×D73 | semidirect |
| 224. #492 | C2×D73 | semidirect |
| 239. #322 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620861 | 2 |
| #22620850 | 2 |
| #22620670 | 2 |
| #22620382 | 2 |
| #22609597 | 2 |
| #22609595 | 2 |
| #22609567 | 2 |
| #22609545 | 2 |
| #22609533 | 2 |
| #22608229 | 2 |
| C73×#1715 | 2 |
| #19727 | 73 |