Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23750349 | C2 | semidirect |
| 3. #23749962 | C2 | semidirect |
| 4. #23749952 | C2 | semidirect |
| 5. #23749907 | C2 | semidirect |
| 6. #23749902 | C2 | semidirect |
| 7. #23749872 | C2 | semidirect |
| 8. C4×#14558725 | C2 | semidirect |
| 9. #23749704 | C2 | semidirect |
| 10. #23749666 | C2 | semidirect |
| 11. #500×C149 | C2 | semidirect |
| 99. C8×C149 | #41 | semidirect |
| 122. C149 | #3353 | semidirect |
| 126. #500 | D149 | semidirect |
| 222. C8 | #14558737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750349 | 2 |
| #23750278 | 2 |
| #23749962 | 2 |
| #23749952 | 2 |
| #23749907 | 2 |
| #23749902 | 2 |
| #23749872 | 2 |
| C4×#14558725 | 2 |
| #23749704 | 2 |
| #23749666 | 2 |
| #500×C149 | 2 |
| #3353 | 149 |