Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752746 | C2 | semidirect |
| 2. #23752599 | C2 | semidirect |
| 3. #23752576 | C2 | semidirect |
| 4. #23752409 | C2 | semidirect |
| 5. #23752404 | C2 | semidirect |
| 6. #23752363 | C2 | semidirect |
| 7. #23752346 | C2 | semidirect |
| 8. #23752269 | C2 | semidirect |
| 9. C2×#127×C151 | C2 | semidirect |
| 10. C2×#14558992 | C22 | semidirect |
| 11. C2×#14558989 | C22 | semidirect |
| 13. #18012731 | C22 | semidirect |
| 14. #18012727 | C22 | semidirect |
| 18. C4×Dic302 | C22 | semidirect |
| 19. C4×D604 | C22 | semidirect |
| 22. C4⋊(C151⋊C8) | C22 | semidirect |
| 23. #18012660 | C22 | semidirect |
| 24. #18012660 | C22 | semidirect |
| 26. #18012650 | C22 | semidirect |
| 127. C151 | #3217 | semidirect |
| 129. C2×#127 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| #23752599 | 2 |
| #23752576 | 2 |
| #23752409 | 2 |
| #23752404 | 2 |
| #23752363 | 2 |
| #23752346 | 2 |
| #23752269 | 2 |
| C2×#127×C151 | 2 |
| #3217 | 151 |