Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1132 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1132 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. #22620846 | C2 | semidirect |
| 2. #22620384 | C2 | semidirect |
| 3. #22609014 | C2 | semidirect |
| 4. #22608985 | C2 | semidirect |
| 5. #22608593 | C2 | semidirect |
| 6. #22608348 | C2 | semidirect |
| 7. C73×#3549 | C2 | semidirect |
| 9. C2×#14556588 | C22 | semidirect |
| 13. #17988961 | C22 | semidirect |
| 15. #17988782 | C22 | semidirect |
| 17. #17988640 | C22 | semidirect |
| 18. C4×#11924012 | C22 | semidirect |
| 19. #17988336 | C22 | semidirect |
| 20. #17988331 | C22 | semidirect |
| 21. D4⋊#10596831 | C22 | semidirect |
| 24. #555×C73 | C22 | semidirect |
| 26. D42×C73 | C22 | semidirect |
| 180. #3549 | D73 | semidirect |
| 187. C73 | #18714 | semidirect |
| 191. #555 | C2×D73 | semidirect |
| 193. D42 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620846 | 2 |
| #22620384 | 2 |
| #22609014 | 2 |
| #22608985 | 2 |
| #22608593 | 2 |
| #22608348 | 2 |
| C73×#3549 | 2 |
| #18714 | 73 |