Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012764 | C2 | semidirect |
| 2. C2×#18012746 | C2 | semidirect |
| 3. #23752776 | C2 | semidirect |
| 4. #23752463 | C2 | semidirect |
| 5. #23752460 | C2 | semidirect |
| 6. #23752446 | C2 | semidirect |
| 7. #23752443 | C2 | semidirect |
| 8. #23752252 | C2 | semidirect |
| 9. #23752208 | C2 | semidirect |
| 10. C2×#18012659 | C2 | semidirect |
| 11. #537×C151 | C2 | semidirect |
| 18. C2×#14558988 | C22 | semidirect |
| 20. C22×C151⋊C8 | C22 | semidirect |
| 27. #18012672 | C22 | semidirect |
| 28. #18012670 | C22 | semidirect |
| 29. #18012663 | C22 | semidirect |
| 30. #18012663 | C22 | semidirect |
| 31. #18012660 | C22 | semidirect |
| 32. #18012660 | C22 | semidirect |
| 38. C22⋊Q8×C151 | C22 | semidirect |
| 41. #121×C151 | C22 | semidirect |
| 53. #14558988 | D4 | semidirect |
| 151. C151 | #3062 | semidirect |
| 155. #537 | D151 | semidirect |
| 178. C22⋊Q8 | C2×D151 | semidirect |
| 183. #121 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012764 | 2 |
| C2×#18012746 | 2 |
| #23752776 | 2 |
| #23752463 | 2 |
| #23752460 | 2 |
| #23752446 | 2 |
| #23752443 | 2 |
| #23752252 | 2 |
| #23752208 | 2 |
| C2×#18012659 | 2 |
| #537×C151 | 2 |
| #3062 | 151 |