Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23750182 | C2 | semidirect |
| 2. #23749929 | C2 | semidirect |
| 3. #23749920 | C2 | semidirect |
| 4. #23749915 | C2 | semidirect |
| 5. #23749881 | C2 | semidirect |
| 7. #23749844 | C2 | semidirect |
| 8. #23749835 | C2 | semidirect |
| 9. #23749830 | C2 | semidirect |
| 10. #23749649 | C2 | semidirect |
| 133. C149 | #3252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750182 | 2 |
| #23749929 | 2 |
| #23749920 | 2 |
| #23749915 | 2 |
| #23749881 | 2 |
| #23749869 | 2 |
| #23749844 | 2 |
| #23749835 | 2 |
| #23749830 | 2 |
| #23749649 | 2 |
| #529×C149 | 2 |
| #3252 | 149 |