Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #22607810 | C2 | semidirect |
| 5. #22607799 | C2 | semidirect |
| 6. #22607798 | C2 | semidirect |
| 7. C73×#1294 | C2 | semidirect |
| 14. #17988454 | C4 | semidirect |
| 15. #17988449 | C4 | semidirect |
| 19. #17988434 | C4 | semidirect |
| 20. #17988432 | C4 | semidirect |
| 232. #1294 | D73 | semidirect |
| 235. C73 | #8762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612867 | 2 |
| #22609916 | 2 |
| #22608247 | 2 |
| #22607810 | 2 |
| #22607799 | 2 |
| #22607798 | 2 |
| C73×#1294 | 2 |
| #8762 | 73 |