Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
338 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23750024 | C2 | semidirect |
| 4. #23750004 | C2 | semidirect |
| 5. #23749994 | C2 | semidirect |
| 8. #23749729 | C2 | semidirect |
| 9. #23749717 | C2 | semidirect |
| 11. #491×C149 | C2 | semidirect |
| 102. C149 | #3177 | semidirect |
| 109. #491 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750238 | 2 |
| #23750236 | 2 |
| #23750024 | 2 |
| #23750004 | 2 |
| #23749994 | 2 |
| #23749882 | 2 |
| #23749865 | 2 |
| #23749729 | 2 |
| #23749717 | 2 |
| #23749582 | 2 |
| #491×C149 | 2 |
| #3177 | 149 |