Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #23750290 | C2 | semidirect |
| 3. #23749964 | C2 | semidirect |
| 4. #23749917 | C2 | semidirect |
| 5. #23749874 | C2 | semidirect |
| 6. #23749827 | C2 | semidirect |
| 7. #23749765 | C2 | semidirect |
| 8. C4×#14558725 | C2 | semidirect |
| 9. #23749704 | C2 | semidirect |
| 10. #23749632 | C2 | semidirect |
| 11. #487×C149 | C2 | semidirect |
| 126. C149 | #3329 | semidirect |
| 130. #487 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750341 | 2 |
| #23750290 | 2 |
| #23749964 | 2 |
| #23749917 | 2 |
| #23749874 | 2 |
| #23749827 | 2 |
| #23749765 | 2 |
| C4×#14558725 | 2 |
| #23749704 | 2 |
| #23749632 | 2 |
| #487×C149 | 2 |
| #3329 | 149 |