Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
788 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 788 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. #22620889 | C2 | semidirect |
| 2. #22620851 | C2 | semidirect |
| 3. #22620669 | C2 | semidirect |
| 4. #22620306 | C2 | semidirect |
| 5. #22609597 | C2 | semidirect |
| 6. #22609591 | C2 | semidirect |
| 7. #22609570 | C2 | semidirect |
| 8. #22609537 | C2 | semidirect |
| 9. C73×#1453 | C2 | semidirect |
| 13. #17988985 | C22 | semidirect |
| 14. #17988967 | C22 | semidirect |
| 17. #17988964 | C22 | semidirect |
| 18. #17988960 | C22 | semidirect |
| 20. #17988938 | C22 | semidirect |
| 25. #17988934 | C22 | semidirect |
| 26. #17988934 | C22 | semidirect |
| 36. #322×C73 | C22 | semidirect |
| 37. #322×C73 | C22 | semidirect |
| 38. C82×C73 | C22 | semidirect |
| 178. #1453 | D73 | semidirect |
| 179. C73 | #19729 | semidirect |
| 206. #322 | C2×D73 | semidirect |
| 207. #322 | C2×D73 | semidirect |
| 208. C82 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620889 | 2 |
| #22620851 | 2 |
| #22620669 | 2 |
| #22620306 | 2 |
| #22609597 | 2 |
| #22609591 | 2 |
| #22609570 | 2 |
| #22609537 | 2 |
| C73×#1453 | 2 |
| #19729 | 73 |