Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22618597 | C2 | semidirect |
| 2. #22618569 | C2 | semidirect |
| 3. #22618564 | C2 | semidirect |
| 4. C2×#17988611 | C2 | semidirect |
| 6. #22618350 | C2 | semidirect |
| 9. #17988648 | C22 | semidirect |
| 10. #17988644 | C22 | semidirect |
| 11. #17988640 | C22 | semidirect |
| 14. #17988611 | C22 | semidirect |
| 15. C2×C4⋊#10596831 | C22 | semidirect |
| 18. #17988543 | C22 | semidirect |
| 187. C73 | #60125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618597 | 2 |
| #22618569 | 2 |
| #22618564 | 2 |
| C2×#17988611 | 2 |
| #22618376 | 2 |
| #22618350 | 2 |
| C2×C4×#41×C73 | 2 |
| #60125 | 73 |