Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
712 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22621092 | C2 | semidirect |
| 3. #22609584 | C2 | semidirect |
| 4. #22609553 | C2 | semidirect |
| 5. #22609543 | C2 | semidirect |
| 6. #22609518 | C2 | semidirect |
| 7. C73×#1454 | C2 | semidirect |
| 10. #17988992 | C22 | semidirect |
| 11. #17988985 | C22 | semidirect |
| 14. #17988938 | C22 | semidirect |
| 15. #17988938 | C22 | semidirect |
| 23. #322×C73 | C22 | semidirect |
| 24. C82×C73 | C22 | semidirect |
| 108. #1454 | D73 | semidirect |
| 109. C73 | #19733 | semidirect |
| 125. #322 | C2×D73 | semidirect |
| 126. C82 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22621092 | 2 |
| #22620874 | 2 |
| #22609584 | 2 |
| #22609553 | 2 |
| #22609543 | 2 |
| #22609518 | 2 |
| C73×#1454 | 2 |
| #19733 | 73 |