Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23753010 | C2 | semidirect |
| 2. C2×#18012767 | C2 | semidirect |
| 3. C2×#18012764 | C2 | semidirect |
| 4. #23752482 | C2 | semidirect |
| 5. #23752475 | C2 | semidirect |
| 6. #23752261 | C2 | semidirect |
| 7. #23752194 | C2 | semidirect |
| 8. C2×#18012655 | C2 | semidirect |
| 9. #568×C151 | C2 | semidirect |
| 13. #18012769 | C22 | semidirect |
| 19. #18012764 | C22 | semidirect |
| 21. C2×#14558993 | C22 | semidirect |
| 23. C2×D1208 | C22 | semidirect |
| 27. #18012675 | C22 | semidirect |
| 28. #18012657 | C22 | semidirect |
| 29. #18012655 | C22 | semidirect |
| 30. #18012655 | C22 | semidirect |
| 33. #131×C151 | C22 | semidirect |
| 147. C151 | #3068 | semidirect |
| 152. #568 | D151 | semidirect |
| 175. #131 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753010 | 2 |
| C2×#18012767 | 2 |
| C2×#18012764 | 2 |
| #23752482 | 2 |
| #23752475 | 2 |
| #23752261 | 2 |
| #23752194 | 2 |
| C2×#18012655 | 2 |
| #568×C151 | 2 |
| #3068 | 151 |