Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
342 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 14. #17989450 | C4 | semidirect |
| 15. #17989449 | C4 | semidirect |
| 23. #17988339 | C4 | semidirect |
| 24. #17988339 | C4 | semidirect |
| 25. #17988338 | C4 | semidirect |
| 26. #334×C73 | C4 | semidirect |
| 136. C73 | #8270 | semidirect |
| 151. #334 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22625644 | 2 |
| #22625481 | 2 |
| #22625147 | 2 |
| #22625137 | 2 |
| #22624758 | 2 |
| #22608676 | 2 |
| #8270 | 73 |