Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
826 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 18. #17988967 | C4 | semidirect |
| 19. #17988966 | C4 | semidirect |
| 20. #17988965 | C4 | semidirect |
| 22. #494×C73 | C4 | semidirect |
| 119. C73 | #22277 | semidirect |
| 126. #494 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626422 | 2 |
| #22626062 | 2 |
| #22625925 | 2 |
| #22625853 | 2 |
| #22625649 | 2 |
| #494×D73 | 2 |
| #22277 | 73 |