Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22624336 | C2 | semidirect |
| 2. #22621309 | C2 | semidirect |
| 3. #22609074 | C2 | semidirect |
| 4. #22609045 | C2 | semidirect |
| 5. #22609012 | C2 | semidirect |
| 6. #22608983 | C2 | semidirect |
| 7. #22608666 | C2 | semidirect |
| 8. #22608383 | C2 | semidirect |
| 9. C73×#3147 | C2 | semidirect |
| 19. #17988874 | C22 | semidirect |
| 22. #17988779 | C22 | semidirect |
| 23. #17988611 | C22 | semidirect |
| 24. #17988336 | C22 | semidirect |
| 26. #17988316 | C22 | semidirect |
| 27. #17988316 | C22 | semidirect |
| 30. #532×C73 | C22 | semidirect |
| 32. #494×C73 | C22 | semidirect |
| 35. #492×C73 | C22 | semidirect |
| 36. C2×C4×C8×C73 | C22 | semidirect |
| 208. #3147 | D73 | semidirect |
| 215. C73 | #18686 | semidirect |
| 226. #532 | C2×D73 | semidirect |
| 228. #494 | C2×D73 | semidirect |
| 231. #492 | C2×D73 | semidirect |
| 238. C2×C4×C8 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624336 | 2 |
| #22621309 | 2 |
| #22609074 | 2 |
| #22609045 | 2 |
| #22609012 | 2 |
| #22608983 | 2 |
| #22608666 | 2 |
| #22608383 | 2 |
| C73×#3147 | 2 |
| #18686 | 73 |