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. #22620677 | C2 | semidirect |
| 2. #22620652 | C2 | semidirect |
| 4. #22620302 | C2 | semidirect |
| 5. #22609600 | C2 | semidirect |
| 6. #22609585 | C2 | semidirect |
| 7. #22609571 | C2 | semidirect |
| 8. #22609560 | C2 | semidirect |
| 9. #22609537 | C2 | semidirect |
| 10. #22608233 | C2 | semidirect |
| 11. C73×#1708 | C2 | semidirect |
| 16. #17988990 | C22 | semidirect |
| 18. #17988967 | C22 | semidirect |
| 22. #17988961 | C22 | semidirect |
| 24. #17988939 | C22 | semidirect |
| 27. #17988934 | C22 | semidirect |
| 36. #17988308 | C22 | semidirect |
| 37. #17988308 | C22 | semidirect |
| 38. #498×C73 | C22 | semidirect |
| 40. #487×C73 | C22 | semidirect |
| 42. C82×C73 | C22 | semidirect |
| 197. #1708 | D73 | semidirect |
| 199. C73 | #19749 | semidirect |
| 205. #498 | C2×D73 | semidirect |
| 215. #487 | 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 |
|---|---|
| #22620677 | 2 |
| #22620652 | 2 |
| #22620378 | 2 |
| #22620302 | 2 |
| #22609600 | 2 |
| #22609585 | 2 |
| #22609571 | 2 |
| #22609560 | 2 |
| #22609537 | 2 |
| #22608233 | 2 |
| C73×#1708 | 2 |
| #19749 | 73 |