Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 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. #23750175 | C2 | semidirect |
| 2. #23750015 | C2 | semidirect |
| 3. #23749984 | C2 | semidirect |
| 4. #23749837 | C2 | semidirect |
| 5. #23749764 | C2 | semidirect |
| 6. #23749759 | C2 | semidirect |
| 7. #23749682 | C2 | semidirect |
| 8. C2×#124×C149 | C2 | semidirect |
| 10. C2×#14558723 | C22 | semidirect |
| 12. #18011911 | C22 | semidirect |
| 13. #18011908 | C22 | semidirect |
| 18. C4×D596 | C22 | semidirect |
| 19. C4⋊#11924746 | C22 | semidirect |
| 20. #18011835 | C22 | semidirect |
| 23. #18011822 | C22 | semidirect |
| 120. C149 | #3213 | semidirect |
| 123. C2×#124 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23750015 | 2 |
| #23749984 | 2 |
| #23749837 | 2 |
| #23749764 | 2 |
| #23749759 | 2 |
| #23749682 | 2 |
| C2×#124×C149 | 2 |
| #3213 | 149 |