Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
990 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 100 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. C2×#17989493 | C2 | semidirect |
| 10. C2×#14556589 | C4 | semidirect |
| 14. C2×#14556550 | C4 | semidirect |
| 15. C23×Q8×C73 | C4 | semidirect |
| 151. C73 | #12698 | semidirect |
| 153. C23×Q8 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989493 | 2 |
| #22625760 | 2 |
| C2×#17989161 | 2 |
| #12698 | 73 |