Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22618911 | C2 | semidirect |
| 3. #22608509 | C2 | semidirect |
| 4. #22608479 | C2 | semidirect |
| 5. #22608347 | C2 | semidirect |
| 6. #22607797 | C2 | semidirect |
| 7. C73×#1287 | C2 | semidirect |
| 10. #17988981 | C4 | semidirect |
| 11. #17988976 | C4 | semidirect |
| 12. #17988956 | C4 | semidirect |
| 13. #17988952 | C4 | semidirect |
| 211. #1287 | D73 | semidirect |
| 212. C73 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620970 | 2 |
| #22618911 | 2 |
| #22608509 | 2 |
| #22608479 | 2 |
| #22608347 | 2 |
| #22607797 | 2 |
| C73×#1287 | 2 |
| #9370 | 73 |