Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
318 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 318 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. C4×#11924003 | C4 | semidirect |
| 18. C16×Dic73 | C4 | semidirect |
| 19. C16×Dic73 | C4 | semidirect |
| 20. C4×C16×C73 | C4 | semidirect |
| 116. C73 | #12670 | semidirect |
| 130. C4×C16 | #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 |
| C4×C16×D73 | 2 |
| #12670 | 73 |