Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
908 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22620645 | C2 | semidirect |
| 2. #22620384 | C2 | semidirect |
| 3. #22620306 | C2 | semidirect |
| 4. #22609596 | C2 | semidirect |
| 5. #22609571 | C2 | semidirect |
| 6. #22609556 | C2 | semidirect |
| 7. #22609522 | C2 | semidirect |
| 8. #22608234 | C2 | semidirect |
| 9. C73×#3184 | C2 | semidirect |
| 13. #17988990 | C22 | semidirect |
| 19. #17988959 | C22 | semidirect |
| 21. #17988939 | C22 | semidirect |
| 24. #17988933 | C22 | semidirect |
| 29. #17988309 | C22 | semidirect |
| 30. #17988308 | C22 | semidirect |
| 31. C8×#10596831 | C22 | semidirect |
| 33. #498×C73 | C22 | semidirect |
| 34. #493×C73 | C22 | semidirect |
| 35. #486×C73 | C22 | semidirect |
| 150. #10596831 | AGL(1,ℤ/8) | semidirect |
| 173. #3184 | D73 | semidirect |
| 182. C73 | #19747 | semidirect |
| 188. #498 | C2×D73 | semidirect |
| 192. #493 | C2×D73 | semidirect |
| 201. #486 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620645 | 2 |
| #22620384 | 2 |
| #22620306 | 2 |
| #22609596 | 2 |
| #22609571 | 2 |
| #22609556 | 2 |
| #22609522 | 2 |
| #22608234 | 2 |
| C73×#3184 | 2 |
| #19747 | 73 |