Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
308 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #22625079 | C2 | semidirect |
| 4. #22625078 | C2 | semidirect |
| 5. #22625060 | C2 | semidirect |
| 6. #22625060 | C2 | semidirect |
| 16. #17989198 | C4 | semidirect |
| 19. #17988955 | C4 | semidirect |
| 25. #17988646 | C4 | semidirect |
| 26. #494×C73 | C4 | semidirect |
| 161. C73 | #13608 | semidirect |
| 165. #494 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626229 | 2 |
| #22626214 | 2 |
| #22625079 | 2 |
| #22625078 | 2 |
| #22625060 | 2 |
| #22621007 | 2 |
| #13608 | 73 |