Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 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. #23750175 | C2 | semidirect |
| 2. #23749922 | C2 | semidirect |
| 3. #23749910 | C2 | semidirect |
| 4. #23749905 | C2 | semidirect |
| 5. #23749876 | C2 | semidirect |
| 6. #23749873 | C2 | semidirect |
| 7. #23749837 | C2 | semidirect |
| 8. #23749825 | C2 | semidirect |
| 9. #23749820 | C2 | semidirect |
| 10. #23749649 | C2 | semidirect |
| 11. #529×C149 | C2 | semidirect |
| 141. C149 | #3251 | semidirect |
| 144. #529 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23749922 | 2 |
| #23749910 | 2 |
| #23749905 | 2 |
| #23749876 | 2 |
| #23749873 | 2 |
| #23749837 | 2 |
| #23749825 | 2 |
| #23749820 | 2 |
| #23749649 | 2 |
| #529×C149 | 2 |
| #3251 | 149 |