Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
822 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 822 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. #22620674 | C2 | semidirect |
| 2. #22620648 | C2 | semidirect |
| 4. #22620302 | C2 | semidirect |
| 5. #22609603 | C2 | semidirect |
| 6. #22609581 | C2 | semidirect |
| 7. #22609567 | C2 | semidirect |
| 8. #22609557 | C2 | semidirect |
| 9. #22609532 | C2 | semidirect |
| 10. #22608233 | C2 | semidirect |
| 11. C73×#1709 | C2 | semidirect |
| 16. #17988990 | C22 | semidirect |
| 17. #17988985 | C22 | semidirect |
| 22. #17988959 | C22 | semidirect |
| 24. #17988938 | C22 | semidirect |
| 25. #17988937 | C22 | semidirect |
| 36. #17988308 | C22 | semidirect |
| 37. #17988308 | C22 | semidirect |
| 38. #494×C73 | C22 | semidirect |
| 41. #486×C73 | C22 | semidirect |
| 42. C82×C73 | C22 | semidirect |
| 196. #1709 | D73 | semidirect |
| 199. C73 | #19749 | semidirect |
| 207. #494 | C2×D73 | semidirect |
| 220. #486 | C2×D73 | semidirect |
| 230. C82 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620674 | 2 |
| #22620648 | 2 |
| #22620382 | 2 |
| #22620302 | 2 |
| #22609603 | 2 |
| #22609581 | 2 |
| #22609567 | 2 |
| #22609557 | 2 |
| #22609532 | 2 |
| #22608233 | 2 |
| C73×#1709 | 2 |
| #19749 | 73 |