Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#14558989 | C2 | semidirect |
| 2. #23752776 | C2 | semidirect |
| 3. #23752687 | C2 | semidirect |
| 4. #23752429 | C2 | semidirect |
| 5. #23752405 | C2 | semidirect |
| 6. #23752240 | C2 | semidirect |
| 7. #23752218 | C2 | semidirect |
| 8. #23752208 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C151 | C2 | semidirect |
| 14. #18012735 | C22 | semidirect |
| 15. #18012728 | C22 | semidirect |
| 19. D4×Dic151 | C22 | semidirect |
| 23. Dic151⋊C8 | C22 | semidirect |
| 24. #18012663 | C22 | semidirect |
| 25. #18012661 | C22 | semidirect |
| 26. #18012660 | C22 | semidirect |
| 30. C2×SD16×C151 | C22 | semidirect |
| 31. C2×D8×C151 | C22 | semidirect |
| 58. C2×D4×C151 | D4 | semidirect |
| 121. C151 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D151 | semidirect |
| 136. C2×SD16 | C2×D151 | semidirect |
| 139. C2×D8 | C2×D151 | semidirect |
| 168. C2×D4 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558989 | 2 |
| #23752776 | 2 |
| #23752687 | 2 |
| #23752429 | 2 |
| #23752405 | 2 |
| #23752240 | 2 |
| #23752218 | 2 |
| #23752208 | 2 |
| C2×AGL(1,ℤ/8)×C151 | 2 |
| #3041 | 151 |