Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012785 | C2 | semidirect |
| 2. C22×#14558989 | C2 | semidirect |
| 3. #23752779 | C2 | semidirect |
| 4. #23752356 | C2 | semidirect |
| 5. #23752344 | C2 | semidirect |
| 6. #23752218 | C2 | semidirect |
| 7. #23752208 | C2 | semidirect |
| 8. #23752180 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C151 | C2 | semidirect |
| 12. C2×#14559005 | C22 | semidirect |
| 18. C2×D4×D151 | C22 | semidirect |
| 20. C2×#14558989 | C22 | semidirect |
| 21. C22×C151⋊C8 | C22 | semidirect |
| 24. #18012710 | C22 | semidirect |
| 26. #18012698 | C22 | semidirect |
| 27. #18012663 | C22 | semidirect |
| 28. #18012661 | C22 | semidirect |
| 29. #18012660 | C22 | semidirect |
| 30. (C2×D151)⋊C8 | C22 | semidirect |
| 32. C22×D4×C151 | C22 | semidirect |
| 34. C2×SD16×C151 | C22 | semidirect |
| 35. C2×D8×C151 | C22 | semidirect |
| 36. C2×M16×C151 | C22 | semidirect |
| 50. C2×D604 | D4 | semidirect |
| 69. #41×C151 | D4 | semidirect |
| 151. C151 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D151 | semidirect |
| 172. C22×D4 | C2×D151 | semidirect |
| 174. C2×SD16 | C2×D151 | semidirect |
| 177. C2×D8 | C2×D151 | semidirect |
| 178. C2×M16 | C2×D151 | semidirect |
| 198. #41 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012785 | 2 |
| C22×#14558989 | 2 |
| #23752779 | 2 |
| #23752356 | 2 |
| #23752344 | 2 |
| #23752218 | 2 |
| #23752208 | 2 |
| #23752180 | 2 |
| C2×AGL(1,ℤ/8)×C151 | 2 |
| #3008 | 151 |