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. #22620859 | C2 | semidirect |
| 2. #22620845 | C2 | semidirect |
| 3. #22620667 | C2 | semidirect |
| 4. #22620382 | C2 | semidirect |
| 5. #22609598 | C2 | semidirect |
| 6. #22609596 | C2 | semidirect |
| 7. #22609569 | C2 | semidirect |
| 8. #22609557 | C2 | semidirect |
| 9. #22609532 | C2 | semidirect |
| 10. #22608225 | C2 | semidirect |
| 11. C73×#1712 | C2 | semidirect |
| 16. #17988985 | C22 | semidirect |
| 22. #17988959 | C22 | semidirect |
| 23. #17988938 | C22 | semidirect |
| 26. #17988933 | C22 | semidirect |
| 27. #17988933 | C22 | semidirect |
| 36. #17988309 | C22 | semidirect |
| 37. #17988308 | C22 | semidirect |
| 40. #493×C73 | C22 | semidirect |
| 41. #493×C73 | C22 | semidirect |
| 42. C82×C73 | C22 | semidirect |
| 206. #1712 | D73 | semidirect |
| 209. C73 | #19727 | semidirect |
| 220. #493 | C2×D73 | semidirect |
| 221. #493 | C2×D73 | semidirect |
| 240. C82 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620859 | 2 |
| #22620845 | 2 |
| #22620667 | 2 |
| #22620382 | 2 |
| #22609598 | 2 |
| #22609596 | 2 |
| #22609569 | 2 |
| #22609557 | 2 |
| #22609532 | 2 |
| #22608225 | 2 |
| C73×#1712 | 2 |
| #19727 | 73 |