Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22621309 | C2 | semidirect |
| 2. #22620357 | C2 | semidirect |
| 3. #22609076 | C2 | semidirect |
| 4. #22609047 | C2 | semidirect |
| 5. #22609014 | C2 | semidirect |
| 6. #22608985 | C2 | semidirect |
| 7. #22608666 | C2 | semidirect |
| 8. #22608382 | C2 | semidirect |
| 9. C73×#3549 | C2 | semidirect |
| 11. #17989137 | C22 | semidirect |
| 13. #17988966 | C22 | semidirect |
| 15. #17988961 | C22 | semidirect |
| 17. #17988877 | C22 | semidirect |
| 20. #17988782 | C22 | semidirect |
| 22. #17988611 | C22 | semidirect |
| 23. C2×C4×#10596831 | C22 | semidirect |
| 24. #17988336 | C22 | semidirect |
| 26. D4⋊#10596831 | C22 | semidirect |
| 27. D4⋊#10596831 | C22 | semidirect |
| 206. #3549 | D73 | semidirect |
| 215. C73 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621309 | 2 |
| #22620357 | 2 |
| #22609076 | 2 |
| #22609047 | 2 |
| #22609014 | 2 |
| #22608985 | 2 |
| #22608666 | 2 |
| #22608382 | 2 |
| C73×#3549 | 2 |
| #18686 | 73 |