Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
766 conjugacy classes of subgroups.
The subgroup lattice has 602 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22608061 | C2 | direct (N × H) |
| 5. C22×#11924012 | C4 | semidirect |
| 6. C23×#10596831 | C4 | semidirect |
| 16. #17988554 | C4 | semidirect |
| 24. #413×C73 | C4 | semidirect |
| 26. C2×#101×C73 | C4 | semidirect |
| 31. C2×#11924012 | C2×C4 | semidirect |
| 37. C22×#10596831 | C2×C4 | semidirect |
| 80. #101×C73 | C2×C4 | semidirect |
| 299. C2×C73 | #1395 | semidirect |
| 305. C73 | C2×#1395 | semidirect |
| 313. #413 | Dic73 | semidirect |
| 315. C2×#101 | Dic73 | semidirect |
| 373. #101 | C2×Dic73 | semidirect |
| 599. C2 | #22608061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17988561 | 2 |
| C2×#17988554 | 2 |
| #22608061 | 2 |
| C2×#413×C73 | 2 |
| C2×#1395 | 73 |