Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2198 conjugacy classes of subgroups.
The subgroup lattice has 446 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626620 | C2 | semidirect |
| 2. #22626611 | C2 | semidirect |
| 3. #22626607 | C2 | semidirect |
| 4. #22626573 | C2 | semidirect |
| 6. #22626495 | C2 | semidirect |
| 9. #17989611 | C22 | semidirect |
| 10. #17989608 | C22 | semidirect |
| 11. #17989607 | C22 | semidirect |
| 12. #17989604 | C22 | semidirect |
| 13. #17989603 | C22 | semidirect |
| 14. #17989593 | C22 | semidirect |
| 15. #17989590 | C22 | semidirect |
| 20. #17989551 | C22 | semidirect |
| 21. C4×#11924037 | C22 | semidirect |
| 39. #14556658 | C23 | semidirect |
| 40. C4⋊#10596833 | C23 | semidirect |
| 43. #14556646 | C23 | semidirect |
| 44. C4×#10596833 | C23 | semidirect |
| 230. C73 | #60124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626620 | 2 |
| #22626611 | 2 |
| #22626607 | 2 |
| #22626573 | 2 |
| C2×#17989557 | 2 |
| #22626495 | 2 |
| C22×#14556547 | 2 |
| #60124 | 73 |