Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
334 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 7. #17989491 | C4 | semidirect |
| 9. #17989445 | C4 | semidirect |
| 12. C2×#14556508 | C4 | semidirect |
| 14. #518×C73 | C4 | semidirect |
| 138. C73 | #7493 | semidirect |
| 140. #518 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989491 | 2 |
| #22625458 | 2 |
| #22610329 | 2 |
| #7493 | 73 |