Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×#18012765 | C2 | semidirect |
| 2. C2×#18012759 | C2 | semidirect |
| 3. #23752692 | C2 | semidirect |
| 4. #23752431 | C2 | semidirect |
| 5. #23752424 | C2 | semidirect |
| 6. #23752409 | C2 | semidirect |
| 7. #23752404 | C2 | semidirect |
| 8. #23752239 | C2 | semidirect |
| 9. #23752213 | C2 | semidirect |
| 10. C2×#18012660 | C2 | semidirect |
| 11. #535×C151 | C2 | semidirect |
| 15. C2×#14558994 | C22 | semidirect |
| 17. C2×#14558992 | C22 | semidirect |
| 18. C2×#14558991 | C22 | semidirect |
| 20. C2×#14558989 | C22 | semidirect |
| 23. C4×Dic302 | C22 | semidirect |
| 24. C4×D604 | C22 | semidirect |
| 29. C4⋊(C151⋊C8) | C22 | semidirect |
| 30. C4⋊(C151⋊C8) | C22 | semidirect |
| 31. #18012663 | C22 | semidirect |
| 34. #18012660 | C22 | semidirect |
| 44. #14559004 | D4 | semidirect |
| 154. C151 | #3045 | semidirect |
| 158. #535 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012765 | 2 |
| C2×#18012759 | 2 |
| #23752692 | 2 |
| #23752431 | 2 |
| #23752424 | 2 |
| #23752409 | 2 |
| #23752404 | 2 |
| #23752239 | 2 |
| #23752213 | 2 |
| C2×#18012660 | 2 |
| #535×C151 | 2 |
| #3045 | 151 |