Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. #23750355 | C2 | semidirect |
| 5. #23749908 | C2 | semidirect |
| 7. #23749832 | C2 | semidirect |
| 8. #23749755 | C2 | semidirect |
| 9. #23749729 | C2 | semidirect |
| 11. #487×C149 | C2 | semidirect |
| 116. C149 | #3369 | semidirect |
| 121. #487 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750355 | 2 |
| #23750349 | 2 |
| #23749986 | 2 |
| #23749912 | 2 |
| #23749908 | 2 |
| #23749850 | 2 |
| #23749832 | 2 |
| #23749755 | 2 |
| #23749729 | 2 |
| C4×#14558725 | 2 |
| #487×C149 | 2 |
| #3369 | 149 |