Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 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. C2×#18012713 | C2 | semidirect |
| 2. #23752545 | C2 | semidirect |
| 3. #23752536 | C2 | semidirect |
| 4. #23752528 | C2 | semidirect |
| 5. #23752446 | C2 | semidirect |
| 6. #23752443 | C2 | semidirect |
| 7. #23752362 | C2 | semidirect |
| 8. #23752357 | C2 | semidirect |
| 9. #23752345 | C2 | semidirect |
| 10. C2×C22⋊(C151⋊C8) | C2 | semidirect |
| 11. #525×C151 | C2 | semidirect |
| 14. C2×#14558991 | C22 | semidirect |
| 15. C2×#14558989 | C22 | semidirect |
| 16. C22×C151⋊C8 | C22 | semidirect |
| 23. #18012672 | C22 | semidirect |
| 24. #18012670 | C22 | semidirect |
| 25. #18012663 | C22 | semidirect |
| 26. #18012660 | C22 | semidirect |
| 27. #18012659 | C22 | semidirect |
| 28. #18012659 | C22 | semidirect |
| 31. C22⋊(C151⋊C8) | C22 | semidirect |
| 32. C2×#41×C151 | C22 | semidirect |
| 36. C22⋊Q8×C151 | C22 | semidirect |
| 38. #121×C151 | C22 | semidirect |
| 42. #117×C151 | C22 | semidirect |
| 158. C151 | #3188 | semidirect |
| 160. #525 | D151 | semidirect |
| 171. C2×#41 | C2×D151 | semidirect |
| 180. C22⋊Q8 | C2×D151 | semidirect |
| 186. #121 | C2×D151 | semidirect |
| 190. #117 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012713 | 2 |
| #23752545 | 2 |
| #23752536 | 2 |
| #23752528 | 2 |
| #23752446 | 2 |
| #23752443 | 2 |
| #23752362 | 2 |
| #23752357 | 2 |
| #23752345 | 2 |
| C2×C22⋊(C151⋊C8) | 2 |
| #525×C151 | 2 |
| #3188 | 151 |