Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
730 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 159 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. #22621083 | C2 | semidirect |
| 3. #22620674 | C2 | semidirect |
| 5. #22609609 | C2 | semidirect |
| 6. #22609581 | C2 | semidirect |
| 7. #22609564 | C2 | semidirect |
| 8. #22609547 | C2 | semidirect |
| 9. #22609530 | C2 | semidirect |
| 10. #22608229 | C2 | semidirect |
| 11. C73×#1722 | C2 | semidirect |
| 181. #1722 | D73 | semidirect |
| 187. C73 | #19731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621083 | 2 |
| #22621064 | 2 |
| #22620674 | 2 |
| #22620385 | 2 |
| #22609609 | 2 |
| #22609581 | 2 |
| #22609564 | 2 |
| #22609547 | 2 |
| #22609530 | 2 |
| #22608229 | 2 |
| C73×#1722 | 2 |
| #19731 | 73 |