Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1702 conjugacy classes of subgroups.
The subgroup lattice has 380 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626844 | C2 | semidirect |
| 2. #22626841 | C2 | semidirect |
| 3. #22626838 | C2 | semidirect |
| 4. #22626732 | C2 | semidirect |
| 8. #17989639 | C22 | semidirect |
| 9. #17989639 | C22 | semidirect |
| 10. #17989637 | C22 | semidirect |
| 11. #17989636 | C22 | semidirect |
| 197. C73 | #60249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626844 | 2 |
| #22626841 | 2 |
| #22626838 | 2 |
| #22626732 | 2 |
| #22626613 | 2 |
| #22626609 | 2 |
| C2×#17989143 | 2 |
| #60249 | 73 |