Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23750249 | C2 | semidirect |
| 2. #23750009 | C2 | semidirect |
| 3. #23749987 | C2 | semidirect |
| 4. #23749872 | C2 | semidirect |
| 5. #23749867 | C2 | semidirect |
| 7. #23749724 | C2 | semidirect |
| 8. #23749719 | C2 | semidirect |
| 9. #23749707 | C2 | semidirect |
| 10. #23749579 | C2 | semidirect |
| 11. #500×C149 | C2 | semidirect |
| 117. C149 | #3175 | semidirect |
| 120. #500 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750249 | 2 |
| #23750009 | 2 |
| #23749987 | 2 |
| #23749872 | 2 |
| #23749867 | 2 |
| #23749862 | 2 |
| #23749724 | 2 |
| #23749719 | 2 |
| #23749707 | 2 |
| #23749579 | 2 |
| #500×C149 | 2 |
| #3175 | 149 |