Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
788 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22620883 | C2 | semidirect |
| 2. #22620849 | C2 | semidirect |
| 3. #22620669 | C2 | semidirect |
| 4. #22609599 | C2 | semidirect |
| 5. #22609593 | C2 | semidirect |
| 6. #22609571 | C2 | semidirect |
| 7. #22609535 | C2 | semidirect |
| 8. #22608228 | C2 | semidirect |
| 9. C73×#3138 | C2 | semidirect |
| 11. #17988985 | C22 | semidirect |
| 12. #17988966 | C22 | semidirect |
| 13. #17988964 | C22 | semidirect |
| 16. #17988961 | C22 | semidirect |
| 17. #17988939 | C22 | semidirect |
| 18. #17988935 | C22 | semidirect |
| 19. #17988934 | C22 | semidirect |
| 29. #17988309 | C22 | semidirect |
| 30. #17988308 | C22 | semidirect |
| 31. C8×#10596831 | C22 | semidirect |
| 173. #3138 | D73 | semidirect |
| 179. C73 | #19729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620883 | 2 |
| #22620849 | 2 |
| #22620669 | 2 |
| #22609599 | 2 |
| #22609593 | 2 |
| #22609571 | 2 |
| #22609535 | 2 |
| #22608228 | 2 |
| C73×#3138 | 2 |
| #19729 | 73 |