Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23752758 | C2 | semidirect |
| 3. C2×D4×Dic151 | C2 | semidirect |
| 4. #23752429 | C2 | semidirect |
| 5. #23752425 | C2 | semidirect |
| 6. #23752415 | C2 | semidirect |
| 7. #23752405 | C2 | semidirect |
| 8. #23752235 | C2 | semidirect |
| 9. #23752214 | C2 | semidirect |
| 10. #23752213 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C151 | C2 | semidirect |
| 18. #18012737 | C22 | semidirect |
| 19. #18012735 | C22 | semidirect |
| 20. #18012728 | C22 | semidirect |
| 21. #18012726 | C22 | semidirect |
| 33. Dic151⋊C8 | C22 | semidirect |
| 34. Dic151⋊C8 | C22 | semidirect |
| 35. #18012664 | C22 | semidirect |
| 36. #18012663 | C22 | semidirect |
| 37. #18012661 | C22 | semidirect |
| 38. #18012660 | C22 | semidirect |
| 84. C2×D4×C151 | D4 | semidirect |
| 158. Dic151 | AGL(1,ℤ/8) | semidirect |
| 166. C151 | #3036 | semidirect |
| 169. C2×AGL(1,ℤ/8) | D151 | semidirect |
| 226. C2×D4 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012765 | 2 |
| #23752758 | 2 |
| C2×D4×Dic151 | 2 |
| #23752429 | 2 |
| #23752425 | 2 |
| #23752415 | 2 |
| #23752405 | 2 |
| #23752235 | 2 |
| #23752214 | 2 |
| #23752213 | 2 |
| C2×AGL(1,ℤ/8)×C151 | 2 |
| #3036 | 151 |