Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
322 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #23750031 | C2 | semidirect |
| 4. #23749995 | C2 | semidirect |
| 5. #23749994 | C2 | semidirect |
| 8. #23749919 | C2 | semidirect |
| 9. #23749909 | C2 | semidirect |
| 11. #501×C149 | C2 | semidirect |
| 120. C149 | #3237 | semidirect |
| 125. #501 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750181 | 2 |
| #23750180 | 2 |
| #23750031 | 2 |
| #23749995 | 2 |
| #23749994 | 2 |
| #23749969 | 2 |
| #23749968 | 2 |
| #23749919 | 2 |
| #23749909 | 2 |
| #23749680 | 2 |
| #501×C149 | 2 |
| #3237 | 149 |