Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
454 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 454 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. #23752743 | C2 | semidirect |
| 2. C2×D4×Dic151 | C2 | semidirect |
| 3. #23752548 | C2 | semidirect |
| 4. #23752528 | C2 | semidirect |
| 5. #23752510 | C2 | semidirect |
| 6. #23752425 | C2 | semidirect |
| 7. #23752363 | C2 | semidirect |
| 8. #23752303 | C2 | semidirect |
| 9. D8×Dic151 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 15. #18012730 | C22 | semidirect |
| 16. #18012726 | C22 | semidirect |
| 19. #18012704 | C22 | semidirect |
| 25. D4×Dic151 | C22 | semidirect |
| 30. #18012673 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012664 | C22 | semidirect |
| 35. #18012660 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 140. C151 | #3105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752743 | 2 |
| C2×D4×Dic151 | 2 |
| #23752548 | 2 |
| #23752528 | 2 |
| #23752510 | 2 |
| #23752425 | 2 |
| #23752363 | 2 |
| #23752303 | 2 |
| D8×Dic151 | 2 |
| #23752262 | 2 |
| #447×C151 | 2 |
| #3105 | 151 |