Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
874 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 874 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. #22620865 | C2 | semidirect |
| 2. #22620845 | C2 | semidirect |
| 3. #22620667 | C2 | semidirect |
| 4. #22620378 | C2 | semidirect |
| 5. #22609598 | C2 | semidirect |
| 6. #22609571 | C2 | semidirect |
| 7. #22609559 | C2 | semidirect |
| 8. #22609545 | C2 | semidirect |
| 9. #22609530 | C2 | semidirect |
| 10. #22608229 | C2 | semidirect |
| 11. C73×#1721 | C2 | semidirect |
| 16. #17988985 | C22 | semidirect |
| 21. #17988963 | C22 | semidirect |
| 23. #17988960 | C22 | semidirect |
| 24. #17988939 | C22 | semidirect |
| 27. #17988933 | C22 | semidirect |
| 36. #17988308 | C22 | semidirect |
| 37. C8×#10596831 | C22 | semidirect |
| 39. #493×C73 | C22 | semidirect |
| 41. #486×C73 | C22 | semidirect |
| 42. #322×C73 | C22 | semidirect |
| 203. #1721 | D73 | semidirect |
| 209. C73 | #19727 | semidirect |
| 221. #493 | C2×D73 | semidirect |
| 229. #486 | C2×D73 | semidirect |
| 239. #322 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620865 | 2 |
| #22620845 | 2 |
| #22620667 | 2 |
| #22620378 | 2 |
| #22609598 | 2 |
| #22609571 | 2 |
| #22609559 | 2 |
| #22609545 | 2 |
| #22609530 | 2 |
| #22608229 | 2 |
| C73×#1721 | 2 |
| #19727 | 73 |