Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#18012764 | C2 | semidirect |
| 2. C22×#14558989 | C2 | semidirect |
| 3. #23752686 | C2 | semidirect |
| 4. #23752424 | C2 | semidirect |
| 5. #23752404 | C2 | semidirect |
| 6. #23752239 | C2 | semidirect |
| 7. #23752217 | C2 | semidirect |
| 8. #23752208 | C2 | semidirect |
| 9. #535×C151 | C2 | semidirect |
| 12. C2×#14558991 | C22 | semidirect |
| 15. C2×#14558989 | C22 | semidirect |
| 18. C4×D604 | C22 | semidirect |
| 22. C4⋊(C151⋊C8) | C22 | semidirect |
| 23. #18012663 | C22 | semidirect |
| 24. #18012660 | C22 | semidirect |
| 25. #18012660 | C22 | semidirect |
| 28. #127×C151 | C22 | semidirect |
| 29. #124×C151 | C22 | semidirect |
| 36. C2×D604 | D4 | semidirect |
| 121. C151 | #3041 | semidirect |
| 125. #535 | D151 | semidirect |
| 142. #127 | C2×D151 | semidirect |
| 143. #124 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012764 | 2 |
| C22×#14558989 | 2 |
| #23752686 | 2 |
| #23752424 | 2 |
| #23752404 | 2 |
| #23752239 | 2 |
| #23752217 | 2 |
| #23752208 | 2 |
| #535×C151 | 2 |
| #3041 | 151 |