Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23752840 | C2 | semidirect |
| 2. #23752576 | C2 | semidirect |
| 3. #23752571 | C2 | semidirect |
| 4. #23752566 | C2 | semidirect |
| 5. #23752558 | C2 | semidirect |
| 6. #23752217 | C2 | semidirect |
| 7. #23752213 | C2 | semidirect |
| 8. #23752208 | C2 | semidirect |
| 9. C2×#18012660 | C2 | semidirect |
| 10. #23752168 | C2 | semidirect |
| 14. #18012739 | C22 | semidirect |
| 16. #18012731 | C22 | semidirect |
| 21. #18012663 | C22 | semidirect |
| 22. #18012663 | C22 | semidirect |
| 23. #18012663 | C22 | semidirect |
| 28. #18012660 | C22 | semidirect |
| 29. #18012660 | C22 | semidirect |
| 30. #18012660 | C22 | semidirect |
| 31. #18012650 | C22 | semidirect |
| 32. C4×C151⋊C8 | C22 | semidirect |
| 135. C151 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752840 | 2 |
| #23752576 | 2 |
| #23752571 | 2 |
| #23752566 | 2 |
| #23752558 | 2 |
| #23752217 | 2 |
| #23752213 | 2 |
| #23752208 | 2 |
| C2×#18012660 | 2 |
| #23752168 | 2 |
| #535×C151 | 2 |
| #3136 | 151 |