Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 444 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. #23752764 | C2 | semidirect |
| 3. #23752548 | C2 | semidirect |
| 4. #23752545 | C2 | semidirect |
| 5. #23752490 | C2 | semidirect |
| 6. #23752415 | C2 | semidirect |
| 8. #23752313 | C2 | semidirect |
| 9. #23752309 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 14. #18012738 | C22 | semidirect |
| 15. #18012737 | C22 | semidirect |
| 19. Q8×Dic151 | C22 | semidirect |
| 21. #18012704 | C22 | semidirect |
| 30. #18012673 | C22 | semidirect |
| 31. #18012672 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012664 | C22 | semidirect |
| 34. #18012663 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 136. C151 | #3110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752764 | 2 |
| C2×D4×Dic151 | 2 |
| #23752548 | 2 |
| #23752545 | 2 |
| #23752490 | 2 |
| #23752415 | 2 |
| #23752363 | 2 |
| #23752313 | 2 |
| #23752309 | 2 |
| #23752266 | 2 |
| #450×C151 | 2 |
| #3110 | 151 |