Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2190 conjugacy classes of subgroups.
The subgroup lattice has 522 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#17989468 | C2 | direct (N × H) |
| 12. C22×#11924037 | C4 | semidirect |
| 13. C22×#11924037 | C4 | semidirect |
| 14. C22×#11924037 | C4 | semidirect |
| 18. C23×#10596833 | C4 | semidirect |
| 19. #17989468 | C22 | direct (N × H) |
| 42. C2×#11924037 | C2×C4 | semidirect |
| 43. C2×#11924037 | C2×C4 | semidirect |
| 44. C2×#11924037 | C2×C4 | semidirect |
| 52. C22×#10596833 | C2×C4 | semidirect |
| 90. #11924037 | C22×C4 | semidirect |
| 96. C2×#10596833 | C22×C4 | semidirect |
| 234. C22×C73 | #344 | semidirect |
| 259. C2×C73 | C2×#344 | semidirect |
| 265. C73 | C22×#344 | semidirect |
| 495. C22 | #17989468 | direct (N × H) |
| 519. C2 | C2×#17989468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924037 | 2 |
| C2×#17989468 | 2 |
| C22×#14556547 | 2 |
| C22×#344 | 73 |