Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 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. #23750161 | C2 | semidirect |
| 2. C2×D4×Dic149 | C2 | semidirect |
| 3. #23749953 | C2 | semidirect |
| 4. #23749939 | C2 | semidirect |
| 5. #23749923 | C2 | semidirect |
| 6. #23749842 | C2 | semidirect |
| 8. #23749734 | C2 | semidirect |
| 9. #23749726 | C2 | semidirect |
| 10. #23749679 | C2 | semidirect |
| 11. #450×C149 | C2 | semidirect |
| 15. #18011902 | C22 | semidirect |
| 16. #18011900 | C22 | semidirect |
| 19. Q8×Dic149 | C22 | semidirect |
| 24. #18011873 | C22 | semidirect |
| 30. #18011845 | C22 | semidirect |
| 31. #18011842 | C22 | semidirect |
| 32. #18011840 | C22 | semidirect |
| 33. #18011835 | C22 | semidirect |
| 34. #18011833 | C22 | semidirect |
| 37. #18011821 | C22 | semidirect |
| 140. C149 | #3114 | semidirect |
| 148. #450 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750161 | 2 |
| C2×D4×Dic149 | 2 |
| #23749953 | 2 |
| #23749939 | 2 |
| #23749923 | 2 |
| #23749842 | 2 |
| #23749759 | 2 |
| #23749734 | 2 |
| #23749726 | 2 |
| #23749679 | 2 |
| #450×C149 | 2 |
| #3114 | 149 |