Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
512 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22620585 | C2 | semidirect |
| 3. #22612150 | C2 | semidirect |
| 4. #22612106 | C2 | semidirect |
| 5. #22612011 | C2 | semidirect |
| 8. #22611825 | C2 | semidirect |
| 9. #22611821 | C2 | semidirect |
| 10. #22611744 | C2 | semidirect |
| 11. C73×#2239 | C2 | semidirect |
| 17. #17988987 | C22 | semidirect |
| 18. #17988965 | C22 | semidirect |
| 26. #17988694 | C22 | semidirect |
| 27. #17988693 | C22 | semidirect |
| 31. #17988411 | C22 | semidirect |
| 32. #17988407 | C22 | semidirect |
| 33. #17988402 | C22 | semidirect |
| 37. #17988364 | C22 | semidirect |
| 40. #365×C73 | C22 | semidirect |
| 41. #362×C73 | C22 | semidirect |
| 201. #2239 | D73 | semidirect |
| 209. C73 | #33693 | semidirect |
| 232. #365 | C2×D73 | semidirect |
| 235. #362 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22620585 | 2 |
| #22618833 | 2 |
| #22612150 | 2 |
| #22612106 | 2 |
| #22612011 | 2 |
| #22611884 | 2 |
| #22611881 | 2 |
| #22611825 | 2 |
| #22611821 | 2 |
| #22611744 | 2 |
| C73×#2239 | 2 |
| #33693 | 73 |