Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 2. C2×#17989030 | C2 | semidirect |
| 3. #22619586 | C2 | semidirect |
| 4. #22611884 | C2 | semidirect |
| 5. #22611668 | C2 | semidirect |
| 6. C73×#2115 | C2 | semidirect |
| 15. C22×Dic292 | C22 | semidirect |
| 18. #17989030 | C22 | semidirect |
| 21. #17988845 | C22 | semidirect |
| 23. #17988625 | C22 | semidirect |
| 25. #17988398 | C22 | semidirect |
| 27. C2×M32×C73 | C22 | semidirect |
| 28. #349×C73 | C22 | semidirect |
| 203. #2115 | D73 | semidirect |
| 204. C73 | #33532 | semidirect |
| 220. C2×M32 | C2×D73 | semidirect |
| 226. #349 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22624705 | 2 |
| C2×#17989030 | 2 |
| #22619586 | 2 |
| #22611884 | 2 |
| #22611668 | 2 |
| C73×#2115 | 2 |
| #33532 | 73 |