Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23752760 | C2 | semidirect |
| 2. #124×D151 | C2 | semidirect |
| 3. #23752599 | C2 | semidirect |
| 4. #23752572 | C2 | semidirect |
| 5. #23752571 | C2 | semidirect |
| 6. #23752429 | C2 | semidirect |
| 7. #23752425 | C2 | semidirect |
| 8. #23752349 | C2 | semidirect |
| 9. #23752344 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #496×C151 | C2 | semidirect |
| 15. C2×#14558992 | C22 | semidirect |
| 17. #18012739 | C22 | semidirect |
| 27. D4×Dic151 | C22 | semidirect |
| 31. Dic151⋊C8 | C22 | semidirect |
| 32. #18012664 | C22 | semidirect |
| 33. #18012663 | C22 | semidirect |
| 37. #18012650 | C22 | semidirect |
| 38. C2×SD16×C151 | C22 | semidirect |
| 40. #127×C151 | C22 | semidirect |
| 42. #97×C151 | C22 | semidirect |
| 150. C151 | #3213 | semidirect |
| 155. #496 | D151 | semidirect |
| 167. C2×SD16 | C2×D151 | semidirect |
| 171. #127 | C2×D151 | semidirect |
| 193. #97 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752760 | 2 |
| #124×D151 | 2 |
| #23752599 | 2 |
| #23752572 | 2 |
| #23752571 | 2 |
| #23752429 | 2 |
| #23752425 | 2 |
| #23752349 | 2 |
| #23752344 | 2 |
| #23752267 | 2 |
| #496×C151 | 2 |
| #3213 | 151 |