Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
994 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22620670 | C2 | semidirect |
| 2. #22620668 | C2 | semidirect |
| 3. #22620382 | C2 | semidirect |
| 4. #22620378 | C2 | semidirect |
| 5. #22609599 | C2 | semidirect |
| 6. #22609597 | C2 | semidirect |
| 7. #22609558 | C2 | semidirect |
| 8. #22609545 | C2 | semidirect |
| 9. #22609519 | C2 | semidirect |
| 10. #22608235 | C2 | semidirect |
| 11. C73×#1715 | C2 | semidirect |
| 17. #17988983 | C22 | semidirect |
| 21. #17988964 | C22 | semidirect |
| 24. #17988963 | C22 | semidirect |
| 28. #17988935 | C22 | semidirect |
| 29. #17988934 | C22 | semidirect |
| 36. #17988309 | C22 | semidirect |
| 37. C8×#10596831 | C22 | semidirect |
| 38. #498×C73 | C22 | semidirect |
| 41. #486×C73 | C22 | semidirect |
| 42. #322×C73 | C22 | semidirect |
| 171. C8×C73 | AGL(1,ℤ/8) | semidirect |
| 173. #10596831 | AGL(1,ℤ/8) | semidirect |
| 208. #1715 | D73 | semidirect |
| 212. C73 | #19745 | semidirect |
| 219. #498 | C2×D73 | semidirect |
| 234. #486 | C2×D73 | semidirect |
| 242. #322 | C2×D73 | semidirect |
| 374. C8 | #14556618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620670 | 2 |
| #22620668 | 2 |
| #22620382 | 2 |
| #22620378 | 2 |
| #22609599 | 2 |
| #22609597 | 2 |
| #22609558 | 2 |
| #22609545 | 2 |
| #22609519 | 2 |
| #22608235 | 2 |
| C73×#1715 | 2 |
| #19745 | 73 |