Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1974 conjugacy classes of subgroups.
The subgroup lattice has 472 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626831 | C2 | semidirect |
| 2. #22626830 | C2 | semidirect |
| 3. #22626829 | C2 | semidirect |
| 4. #22626826 | C2 | semidirect |
| 5. #22626732 | C2 | semidirect |
| 9. #17989639 | C22 | semidirect |
| 10. #17989637 | C22 | semidirect |
| 11. #17989636 | C22 | semidirect |
| 107. C2×Dic146 | M16 | semidirect |
| 244. C73 | #60248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626831 | 2 |
| #22626830 | 2 |
| #22626829 | 2 |
| #22626826 | 2 |
| #22626732 | 2 |
| #22626607 | 2 |
| C22×#14556556 | 2 |
| #60248 | 73 |