Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22618495 | C2 | direct (N × H) |
| 3. C2×#17988614 | C2 | semidirect |
| 4. C2×#17988611 | C2 | semidirect |
| 11. #17988614 | C22 | semidirect |
| 12. #17988611 | C22 | semidirect |
| 13. C2×C4⋊#10596831 | C22 | semidirect |
| 30. C4⋊#10596831 | C23 | semidirect |
| 137. C2×C73 | #2905 | semidirect |
| 145. C73 | C2×#2905 | semidirect |
| 276. C2 | #22618495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11924012 | 2 |
| #22618495 | 2 |
| C2×#17988614 | 2 |
| C2×#17988611 | 2 |
| C22×#117×C73 | 2 |
| C2×#2905 | 73 |