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×#18012747 | C2 | semidirect |
| 2. #23752790 | C2 | semidirect |
| 3. #23752779 | C2 | semidirect |
| 4. #23752462 | C2 | semidirect |
| 5. #23752455 | C2 | semidirect |
| 6. #23752445 | C2 | semidirect |
| 7. #23752438 | C2 | semidirect |
| 8. #23752254 | C2 | semidirect |
| 9. #23752208 | C2 | semidirect |
| 10. C2×#18012660 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C151 | C2 | semidirect |
| 14. C2×#14558987 | C22 | semidirect |
| 16. C2×C8×D151 | C22 | semidirect |
| 20. #18012715 | C22 | semidirect |
| 25. #18012710 | C22 | semidirect |
| 29. #18012673 | C22 | semidirect |
| 30. #18012671 | C22 | semidirect |
| 31. #18012663 | C22 | semidirect |
| 32. #18012663 | C22 | semidirect |
| 35. #18012660 | C22 | semidirect |
| 36. #18012660 | C22 | semidirect |
| 83. M16×C151 | D4 | semidirect |
| 151. C151 | #3062 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D151 | semidirect |
| 220. M16 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012747 | 2 |
| #23752790 | 2 |
| #23752779 | 2 |
| #23752462 | 2 |
| #23752455 | 2 |
| #23752445 | 2 |
| #23752438 | 2 |
| #23752254 | 2 |
| #23752208 | 2 |
| C2×#18012660 | 2 |
| C2×AGL(1,ℤ/8)×C151 | 2 |
| #3062 | 151 |