Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23750253 | C2 | semidirect |
| 2. #23749989 | C2 | semidirect |
| 3. #23749984 | C2 | semidirect |
| 4. #23749979 | C2 | semidirect |
| 5. #23749971 | C2 | semidirect |
| 6. #23749630 | C2 | semidirect |
| 7. #23749626 | C2 | semidirect |
| 8. #23749621 | C2 | semidirect |
| 9. C2×#18011832 | C2 | semidirect |
| 10. #23749581 | C2 | semidirect |
| 14. #18011911 | C22 | semidirect |
| 16. #18011903 | C22 | semidirect |
| 21. #18011835 | C22 | semidirect |
| 22. #18011835 | C22 | semidirect |
| 23. #18011835 | C22 | semidirect |
| 28. #18011832 | C22 | semidirect |
| 29. #18011832 | C22 | semidirect |
| 30. #18011832 | C22 | semidirect |
| 31. #18011822 | C22 | semidirect |
| 32. C4×#11924746 | C22 | semidirect |
| 135. C149 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750253 | 2 |
| #23749989 | 2 |
| #23749984 | 2 |
| #23749979 | 2 |
| #23749971 | 2 |
| #23749630 | 2 |
| #23749626 | 2 |
| #23749621 | 2 |
| C2×#18011832 | 2 |
| #23749581 | 2 |
| #535×C149 | 2 |
| #3136 | 149 |