Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
310 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 9. #17989516 | C4 | semidirect |
| 10. #17989515 | C4 | semidirect |
| 11. #17989514 | C4 | semidirect |
| 12. #17989513 | C4 | semidirect |
| 17. #17988363 | C4 | semidirect |
| 18. #17988362 | C4 | semidirect |
| 19. #17988362 | C4 | semidirect |
| 20. #346×C73 | C4 | semidirect |
| 112. C73 | #12671 | semidirect |
| 126. #346 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D73⋊#368 | 2 |
| #22626282 | 2 |
| #22625733 | 2 |
| #22624993 | 2 |
| #346×D73 | 2 |
| #12671 | 73 |