Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
284 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 284 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. #17989493 | C4 | semidirect |
| 9. #17989443 | C4 | semidirect |
| 12. C2×#14556510 | C4 | semidirect |
| 14. #519×C73 | C4 | semidirect |
| 125. C73 | #7481 | semidirect |
| 127. #519 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989493 | 2 |
| #22625412 | 2 |
| #22610334 | 2 |
| #7481 | 73 |