Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
914 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 9. #17989580 | C4 | semidirect |
| 18. #17988494 | C4 | semidirect |
| 19. #17988493 | C4 | semidirect |
| 20. #17988492 | C4 | semidirect |
| 23. #391×C73 | C4 | semidirect |
| 218. C73 | #10947 | semidirect |
| 233. #391 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989580 | 2 |
| #22626497 | 2 |
| #22625631 | 2 |
| C2×#17989454 | 2 |
| #22612514 | 2 |
| #10947 | 73 |