Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 1. #23750180 | C2 | semidirect |
| 3. #23750017 | C2 | semidirect |
| 4. #23749985 | C2 | semidirect |
| 5. #23749984 | C2 | semidirect |
| 6. #23749833 | C2 | semidirect |
| 7. #23749823 | C2 | semidirect |
| 8. #23749786 | C2 | semidirect |
| 9. #23749784 | C2 | semidirect |
| 10. #23749680 | C2 | semidirect |
| 11. #497×C149 | C2 | semidirect |
| 141. C149 | #3216 | semidirect |
| 146. #497 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750180 | 2 |
| #23750174 | 2 |
| #23750017 | 2 |
| #23749985 | 2 |
| #23749984 | 2 |
| #23749833 | 2 |
| #23749823 | 2 |
| #23749786 | 2 |
| #23749784 | 2 |
| #23749680 | 2 |
| #497×C149 | 2 |
| #3216 | 149 |