Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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×#18011890 | C2 | semidirect |
| 2. #23749966 | C2 | semidirect |
| 3. #23749953 | C2 | semidirect |
| 4. #23749936 | C2 | semidirect |
| 5. #23749864 | C2 | semidirect |
| 6. #23749852 | C2 | semidirect |
| 7. #23749787 | C2 | semidirect |
| 8. #23749780 | C2 | semidirect |
| 9. #23749763 | C2 | semidirect |
| 10. C2×C22⋊#11924746 | C2 | semidirect |
| 13. C2×#14558726 | C22 | semidirect |
| 14. C2×#14558724 | C22 | semidirect |
| 23. #18011844 | C22 | semidirect |
| 24. #18011842 | C22 | semidirect |
| 25. #18011835 | C22 | semidirect |
| 26. #18011834 | C22 | semidirect |
| 27. #18011834 | C22 | semidirect |
| 28. #18011832 | C22 | semidirect |
| 149. C149 | #3190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011890 | 2 |
| #23749966 | 2 |
| #23749953 | 2 |
| #23749936 | 2 |
| #23749864 | 2 |
| #23749852 | 2 |
| #23749787 | 2 |
| #23749780 | 2 |
| #23749763 | 2 |
| C2×C22⋊#11924746 | 2 |
| #525×C149 | 2 |
| #3190 | 149 |