Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1244 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 1244 conjugacy classes of subgroups — too many to draw. Only its 228 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 |
|---|---|---|
| 1. #22626863 | C2 | semidirect |
| 2. #22625468 | C2 | semidirect |
| 3. #22625438 | C2 | semidirect |
| 4. #22625434 | C2 | semidirect |
| 8. #17989604 | C22 | semidirect |
| 9. #17989590 | C22 | semidirect |
| 10. #17989447 | C22 | semidirect |
| 11. #17989447 | C22 | semidirect |
| 12. #17989445 | C22 | semidirect |
| 13. #17989445 | C22 | semidirect |
| 157. C73 | #17782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626863 | 2 |
| #22625468 | 2 |
| #22625438 | 2 |
| #22625434 | 2 |
| #22623705 | 2 |
| #17782 | 73 |