Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
292 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 14. #17989516 | C4 | semidirect |
| 15. #17989515 | C4 | semidirect |
| 16. #17989478 | C4 | semidirect |
| 17. #17989477 | C4 | semidirect |
| 23. #17988411 | C4 | semidirect |
| 24. #17988410 | C4 | semidirect |
| 25. #17988409 | C4 | semidirect |
| 26. #365×C73 | C4 | semidirect |
| 140. C73 | #12678 | semidirect |
| 155. #365 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626287 | 2 |
| #22626146 | 2 |
| #22625752 | 2 |
| #22625739 | 2 |
| #22625013 | 2 |
| #22625010 | 2 |
| #22611702 | 2 |
| #12678 | 73 |