Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23750004 | C2 | semidirect |
| 5. #23749835 | C2 | semidirect |
| 6. #23749832 | C2 | semidirect |
| 8. #23749756 | C2 | semidirect |
| 9. #23749730 | C2 | semidirect |
| 11. #557×C149 | C2 | semidirect |
| 119. C149 | #3398 | semidirect |
| 121. #557 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750348 | 2 |
| #23750017 | 2 |
| #23750004 | 2 |
| #23749847 | 2 |
| #23749835 | 2 |
| #23749832 | 2 |
| #23749827 | 2 |
| #23749756 | 2 |
| #23749730 | 2 |
| C4×#14558723 | 2 |
| #557×C149 | 2 |
| #3398 | 149 |