Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22620661 | C2 | semidirect |
| 2. #22618841 | C2 | semidirect |
| 3. #22612148 | C2 | semidirect |
| 4. #22612146 | C2 | semidirect |
| 5. #22612105 | C2 | semidirect |
| 6. #22612002 | C2 | semidirect |
| 8. #22611826 | C2 | semidirect |
| 9. #22611823 | C2 | semidirect |
| 10. #22611740 | C2 | semidirect |
| 11. C73×#2191 | C2 | semidirect |
| 15. #17988987 | C22 | semidirect |
| 16. #17988972 | C22 | semidirect |
| 24. #17988698 | C22 | semidirect |
| 25. #17988694 | C22 | semidirect |
| 30. #17988410 | C22 | semidirect |
| 31. #17988409 | C22 | semidirect |
| 32. #17988407 | C22 | semidirect |
| 33. #17988403 | C22 | semidirect |
| 34. #17988401 | C22 | semidirect |
| 37. #17988364 | C22 | semidirect |
| 205. #2191 | D73 | semidirect |
| 210. C73 | #33690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620661 | 2 |
| #22618841 | 2 |
| #22612148 | 2 |
| #22612146 | 2 |
| #22612105 | 2 |
| #22612002 | 2 |
| #22611877 | 2 |
| #22611826 | 2 |
| #22611823 | 2 |
| #22611740 | 2 |
| C73×#2191 | 2 |
| #33690 | 73 |