Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
520 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22620677 | C2 | semidirect |
| 3. #22612152 | C2 | semidirect |
| 4. #22612099 | C2 | semidirect |
| 5. #22612013 | C2 | semidirect |
| 6. #22612012 | C2 | semidirect |
| 8. #22611821 | C2 | semidirect |
| 9. #22611819 | C2 | semidirect |
| 10. #22611742 | C2 | semidirect |
| 11. C73×#2230 | C2 | semidirect |
| 17. #17988967 | C22 | semidirect |
| 27. #17988693 | C22 | semidirect |
| 31. #17988409 | C22 | semidirect |
| 32. #17988408 | C22 | semidirect |
| 33. #17988404 | C22 | semidirect |
| 34. #17988402 | C22 | semidirect |
| 37. #17988364 | C22 | semidirect |
| 38. #498×C73 | C22 | semidirect |
| 40. #365×C73 | C22 | semidirect |
| 41. #364×C73 | C22 | semidirect |
| 217. #2230 | D73 | semidirect |
| 224. C73 | #33689 | semidirect |
| 230. #498 | C2×D73 | semidirect |
| 247. #365 | C2×D73 | semidirect |
| 249. #364 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620677 | 2 |
| #22618836 | 2 |
| #22612152 | 2 |
| #22612099 | 2 |
| #22612013 | 2 |
| #22612012 | 2 |
| #22611883 | 2 |
| #22611821 | 2 |
| #22611819 | 2 |
| #22611742 | 2 |
| C73×#2230 | 2 |
| #33689 | 73 |