Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #22618951 | C2 | semidirect |
| 3. #22608522 | C2 | semidirect |
| 4. #22608438 | C2 | semidirect |
| 5. #22607824 | C2 | semidirect |
| 6. #22607803 | C2 | semidirect |
| 7. C73×#1759 | C2 | semidirect |
| 10. #17988872 | C4 | semidirect |
| 11. #17988867 | C4 | semidirect |
| 12. #17988787 | C4 | semidirect |
| 13. #17988782 | C4 | semidirect |
| 205. #1759 | D73 | semidirect |
| 210. C73 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620082 | 2 |
| #22618951 | 2 |
| #22608522 | 2 |
| #22608438 | 2 |
| #22607824 | 2 |
| #22607803 | 2 |
| C73×#1759 | 2 |
| #9162 | 73 |