Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
536 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 536 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. #22620576 | C2 | semidirect |
| 2. #22618834 | C2 | semidirect |
| 3. #22612146 | C2 | semidirect |
| 4. #22612143 | C2 | semidirect |
| 5. #22612105 | C2 | semidirect |
| 6. #22612005 | C2 | semidirect |
| 7. #22611877 | C2 | semidirect |
| 8. #22611830 | C2 | semidirect |
| 9. #22611826 | C2 | semidirect |
| 10. #22611744 | C2 | semidirect |
| 11. C73×#2190 | C2 | semidirect |
| 15. #17988987 | C22 | semidirect |
| 16. #17988962 | C22 | semidirect |
| 24. #17988699 | C22 | semidirect |
| 25. #17988698 | C22 | semidirect |
| 30. #17988410 | C22 | semidirect |
| 31. #17988409 | C22 | semidirect |
| 32. #17988407 | C22 | semidirect |
| 33. #17988401 | C22 | semidirect |
| 34. #17988400 | C22 | semidirect |
| 37. #17988364 | C22 | semidirect |
| 217. #2190 | D73 | semidirect |
| 221. C73 | #33692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620576 | 2 |
| #22618834 | 2 |
| #22612146 | 2 |
| #22612143 | 2 |
| #22612105 | 2 |
| #22612005 | 2 |
| #22611877 | 2 |
| #22611830 | 2 |
| #22611826 | 2 |
| #22611744 | 2 |
| C73×#2190 | 2 |
| #33692 | 73 |