Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
2810 conjugacy classes of subgroups.
The subgroup lattice has 298 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22618499 | C2 | direct (N × H) |
| 3. C2×#17988614 | C2 | semidirect |
| 4. C2×#17988611 | C2 | semidirect |
| 5. C22×C4⋊#10596831 | C2 | semidirect |
| 11. #17988614 | C22 | semidirect |
| 12. #17988611 | C22 | semidirect |
| 17. C2×C4⋊#10596831 | C22 | semidirect |
| 113. C2×C4×C73 | #131 | semidirect |
| 140. C4×C73 | C2×#131 | semidirect |
| 145. C2×C73 | #2906 | semidirect |
| 155. C73 | C2×#2906 | semidirect |
| 262. C2×C4 | #14556598 | semidirect |
| 289. C4 | C2×#14556598 | semidirect |
| 293. C2 | #22618499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556598 | 2 |
| #22618499 | 2 |
| C2×#17988614 | 2 |
| C2×#17988611 | 2 |
| C22×C4⋊#10596831 | 2 |
| C2×C4×#41×C73 | 2 |
| C2×#2906 | 73 |