Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #23750175 | C2 | semidirect |
| 2. #23750020 | C2 | semidirect |
| 3. #23750015 | C2 | semidirect |
| 4. #23749995 | C2 | semidirect |
| 5. #23749991 | C2 | semidirect |
| 6. #23749847 | C2 | semidirect |
| 7. #23749840 | C2 | semidirect |
| 8. #23749785 | C2 | semidirect |
| 9. #23749768 | C2 | semidirect |
| 10. #23749682 | C2 | semidirect |
| 11. #529×C149 | C2 | semidirect |
| 140. C149 | #3219 | semidirect |
| 143. #529 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23750020 | 2 |
| #23750015 | 2 |
| #23749995 | 2 |
| #23749991 | 2 |
| #23749847 | 2 |
| #23749840 | 2 |
| #23749785 | 2 |
| #23749768 | 2 |
| #23749682 | 2 |
| #529×C149 | 2 |
| #3219 | 149 |