Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23750173 | C2 | semidirect |
| 2. #23750154 | C2 | semidirect |
| 3. #23750020 | C2 | semidirect |
| 4. #23749994 | C2 | semidirect |
| 5. #23749989 | C2 | semidirect |
| 6. #23749845 | C2 | semidirect |
| 7. #23749838 | C2 | semidirect |
| 8. #23749784 | C2 | semidirect |
| 9. #23749767 | C2 | semidirect |
| 10. #23749680 | C2 | semidirect |
| 11. #496×C149 | C2 | semidirect |
| 140. C149 | #3219 | semidirect |
| 145. #496 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750173 | 2 |
| #23750154 | 2 |
| #23750020 | 2 |
| #23749994 | 2 |
| #23749989 | 2 |
| #23749845 | 2 |
| #23749838 | 2 |
| #23749784 | 2 |
| #23749767 | 2 |
| #23749680 | 2 |
| #496×C149 | 2 |
| #3219 | 149 |