Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
908 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22620669 | C2 | semidirect |
| 2. #22620650 | C2 | semidirect |
| 3. #22620381 | C2 | semidirect |
| 4. #22609599 | C2 | semidirect |
| 5. #22609567 | C2 | semidirect |
| 6. #22609552 | C2 | semidirect |
| 7. #22609522 | C2 | semidirect |
| 8. #22608234 | C2 | semidirect |
| 9. C73×#3138 | C2 | semidirect |
| 12. #17988990 | C22 | semidirect |
| 13. #17988985 | C22 | semidirect |
| 15. #17988964 | C22 | semidirect |
| 18. #17988961 | C22 | semidirect |
| 21. #17988937 | C22 | semidirect |
| 22. #17988935 | C22 | semidirect |
| 23. #17988934 | C22 | semidirect |
| 29. #17988309 | C22 | semidirect |
| 30. #17988308 | C22 | semidirect |
| 31. C8×#10596831 | C22 | semidirect |
| 150. #10596831 | AGL(1,ℤ/8) | semidirect |
| 176. #3138 | D73 | semidirect |
| 182. C73 | #19747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620669 | 2 |
| #22620650 | 2 |
| #22620381 | 2 |
| #22609599 | 2 |
| #22609567 | 2 |
| #22609552 | 2 |
| #22609522 | 2 |
| #22608234 | 2 |
| C73×#3138 | 2 |
| #19747 | 73 |