Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #22610080 | C2 | semidirect |
| 3. #22607926 | C2 | semidirect |
| 5. #22607920 | C2 | semidirect |
| 7. C73×#2165 | C2 | semidirect |
| 9. #17988989 | C4 | semidirect |
| 10. #17988971 | C4 | semidirect |
| 15. #17988700 | C4 | semidirect |
| 16. #17988695 | C4 | semidirect |
| 141. #2165 | D73 | semidirect |
| 147. C73 | #11836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620660 | 2 |
| #22610080 | 2 |
| #22607926 | 2 |
| #22607923 | 2 |
| #22607920 | 2 |
| #22607917 | 2 |
| C73×#2165 | 2 |
| #11836 | 73 |