Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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×#18012762 | C2 | semidirect |
| 2. C2×D8×D151 | C2 | semidirect |
| 3. #23752855 | C2 | semidirect |
| 4. #23752450 | C2 | semidirect |
| 5. #23752445 | C2 | semidirect |
| 6. #23752424 | C2 | semidirect |
| 7. #23752361 | C2 | semidirect |
| 8. #23752356 | C2 | semidirect |
| 9. C4×D1208 | C2 | semidirect |
| 10. C8×D604 | C2 | semidirect |
| 11. #495×C151 | C2 | semidirect |
| 12. C2×#14559005 | C22 | semidirect |
| 15. C2×#14558991 | C22 | semidirect |
| 20. C2×C8×D151 | C22 | semidirect |
| 24. #18012710 | C22 | semidirect |
| 27. C4×D604 | C22 | semidirect |
| 29. #18012673 | C22 | semidirect |
| 30. C4⋊(C151⋊C8) | C22 | semidirect |
| 31. #18012663 | C22 | semidirect |
| 32. #18012661 | C22 | semidirect |
| 33. #18012660 | C22 | semidirect |
| 35. (C2×D151)⋊C8 | C22 | semidirect |
| 36. C2×Q16×C151 | C22 | semidirect |
| 37. C2×SD16×C151 | C22 | semidirect |
| 39. #124×C151 | C22 | semidirect |
| 40. C4×C8×C151 | C22 | semidirect |
| 56. D1208 | D4 | semidirect |
| 127. C2×D151 | #135 | semidirect |
| 143. C151 | #3280 | semidirect |
| 148. #495 | D151 | semidirect |
| 159. C2×Q16 | C2×D151 | semidirect |
| 161. C2×SD16 | C2×D151 | semidirect |
| 168. #124 | C2×D151 | semidirect |
| 184. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012762 | 2 |
| C2×D8×D151 | 2 |
| #23752855 | 2 |
| #23752450 | 2 |
| #23752445 | 2 |
| #23752424 | 2 |
| #23752361 | 2 |
| #23752356 | 2 |
| C4×D1208 | 2 |
| C8×D604 | 2 |
| #495×C151 | 2 |
| #3280 | 151 |