Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752723 | C2 | semidirect |
| 2. #23752542 | C2 | semidirect |
| 3. #23752533 | C2 | semidirect |
| 4. #23752525 | C2 | semidirect |
| 5. #23752463 | C2 | semidirect |
| 6. #23752456 | C2 | semidirect |
| 7. #23752363 | C2 | semidirect |
| 8. #23752355 | C2 | semidirect |
| 9. #23752346 | C2 | semidirect |
| 10. #23752176 | C2 | semidirect |
| 11. C2×#121×C151 | C2 | semidirect |
| 12. C2×#14559004 | C22 | semidirect |
| 13. C2×#14558992 | C22 | semidirect |
| 14. C2×#14558989 | C22 | semidirect |
| 15. C2×#14558988 | C22 | semidirect |
| 18. #18012718 | C22 | semidirect |
| 20. #18012713 | C22 | semidirect |
| 24. #18012698 | C22 | semidirect |
| 25. #18012672 | C22 | semidirect |
| 26. #18012670 | C22 | semidirect |
| 27. #18012662 | C22 | semidirect |
| 28. #18012660 | C22 | semidirect |
| 29. #18012660 | C22 | semidirect |
| 30. #18012659 | C22 | semidirect |
| 33. C22⋊(C151⋊C8) | C22 | semidirect |
| 158. C151 | #3194 | semidirect |
| 161. C2×#121 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752723 | 2 |
| #23752542 | 2 |
| #23752533 | 2 |
| #23752525 | 2 |
| #23752463 | 2 |
| #23752456 | 2 |
| #23752363 | 2 |
| #23752355 | 2 |
| #23752346 | 2 |
| #23752176 | 2 |
| C2×#121×C151 | 2 |
| #3194 | 151 |