Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#18011885 | C2 | semidirect |
| 2. #23749958 | C2 | semidirect |
| 3. #23749949 | C2 | semidirect |
| 4. #23749941 | C2 | semidirect |
| 5. #23749859 | C2 | semidirect |
| 6. #23749856 | C2 | semidirect |
| 7. #23749775 | C2 | semidirect |
| 8. #23749770 | C2 | semidirect |
| 9. #23749758 | C2 | semidirect |
| 10. C2×C22⋊#11924746 | C2 | semidirect |
| 11. #525×C149 | C2 | semidirect |
| 14. C2×#14558723 | C22 | semidirect |
| 15. C2×#14558721 | C22 | semidirect |
| 16. C22×#11924746 | C22 | semidirect |
| 23. #18011844 | C22 | semidirect |
| 24. #18011842 | C22 | semidirect |
| 25. #18011835 | C22 | semidirect |
| 26. #18011832 | C22 | semidirect |
| 27. #18011831 | C22 | semidirect |
| 28. #18011831 | C22 | semidirect |
| 31. C22⋊#11924746 | C22 | semidirect |
| 32. C2×#41×C149 | C22 | semidirect |
| 36. C22⋊Q8×C149 | C22 | semidirect |
| 38. #121×C149 | C22 | semidirect |
| 42. #117×C149 | C22 | semidirect |
| 158. C149 | #3188 | semidirect |
| 160. #525 | D149 | semidirect |
| 171. C2×#41 | C2×D149 | semidirect |
| 180. C22⋊Q8 | C2×D149 | semidirect |
| 186. #121 | C2×D149 | semidirect |
| 190. #117 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011885 | 2 |
| #23749958 | 2 |
| #23749949 | 2 |
| #23749941 | 2 |
| #23749859 | 2 |
| #23749856 | 2 |
| #23749775 | 2 |
| #23749770 | 2 |
| #23749758 | 2 |
| C2×C22⋊#11924746 | 2 |
| #525×C149 | 2 |
| #3188 | 149 |