Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1078 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22620926 | C2 | semidirect |
| 2. #22620376 | C2 | semidirect |
| 3. #22609237 | C2 | semidirect |
| 4. #22609220 | C2 | semidirect |
| 5. #22608566 | C2 | semidirect |
| 6. #22608542 | C2 | semidirect |
| 7. C73×#3549 | C2 | semidirect |
| 9. #17989137 | C22 | semidirect |
| 10. #17988982 | C22 | semidirect |
| 12. #17988977 | C22 | semidirect |
| 13. #17988977 | C22 | semidirect |
| 15. #17988946 | C22 | semidirect |
| 19. #17988644 | C22 | semidirect |
| 20. C2×#14556502 | C22 | semidirect |
| 21. #17988327 | C22 | semidirect |
| 22. #17988327 | C22 | semidirect |
| 191. #3549 | D73 | semidirect |
| 198. C73 | #19052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620926 | 2 |
| #22620376 | 2 |
| #22609237 | 2 |
| #22609220 | 2 |
| #22608566 | 2 |
| #22608542 | 2 |
| C73×#3549 | 2 |
| #19052 | 73 |