Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
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×#14558721 | C2 | semidirect |
| 2. #23750189 | C2 | semidirect |
| 3. #23750100 | C2 | semidirect |
| 4. #23749842 | C2 | semidirect |
| 5. #23749818 | C2 | semidirect |
| 6. #23749653 | C2 | semidirect |
| 7. #23749631 | C2 | semidirect |
| 8. #23749621 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C149 | C2 | semidirect |
| 14. #18011907 | C22 | semidirect |
| 15. #18011900 | C22 | semidirect |
| 19. D4×Dic149 | C22 | semidirect |
| 23. #18011840 | C22 | semidirect |
| 24. #18011835 | C22 | semidirect |
| 25. #18011833 | C22 | semidirect |
| 26. #18011832 | C22 | semidirect |
| 30. C2×SD16×C149 | C22 | semidirect |
| 31. C2×D8×C149 | C22 | semidirect |
| 58. C2×D4×C149 | D4 | semidirect |
| 121. C149 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D149 | semidirect |
| 136. C2×SD16 | C2×D149 | semidirect |
| 139. C2×D8 | C2×D149 | semidirect |
| 168. C2×D4 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558721 | 2 |
| #23750189 | 2 |
| #23750100 | 2 |
| #23749842 | 2 |
| #23749818 | 2 |
| #23749653 | 2 |
| #23749631 | 2 |
| #23749621 | 2 |
| C2×AGL(1,ℤ/8)×C149 | 2 |
| #3041 | 149 |