Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23750162 | C2 | semidirect |
| 2. #23750025 | C2 | semidirect |
| 3. #23750010 | C2 | semidirect |
| 4. #23749981 | C2 | semidirect |
| 5. #23749880 | C2 | semidirect |
| 7. #23749874 | C2 | semidirect |
| 8. #23749738 | C2 | semidirect |
| 9. #23749723 | C2 | semidirect |
| 10. #23749577 | C2 | semidirect |
| 11. #441×C149 | C2 | semidirect |
| 109. C149 | #3183 | semidirect |
| 119. #441 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750162 | 2 |
| #23750025 | 2 |
| #23750010 | 2 |
| #23749981 | 2 |
| #23749880 | 2 |
| #23749879 | 2 |
| #23749874 | 2 |
| #23749738 | 2 |
| #23749723 | 2 |
| #23749577 | 2 |
| #441×C149 | 2 |
| #3183 | 149 |