Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 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. #23750180 | C2 | semidirect |
| 3. #23749988 | C2 | semidirect |
| 4. #23749973 | C2 | semidirect |
| 5. #23749972 | C2 | semidirect |
| 6. #23749971 | C2 | semidirect |
| 7. #23749628 | C2 | semidirect |
| 8. C4×#14558719 | C2 | semidirect |
| 9. #486×C149 | C2 | semidirect |
| 14. #18011911 | C22 | semidirect |
| 19. #18011902 | C22 | semidirect |
| 26. #18011833 | C22 | semidirect |
| 27. #18011832 | C22 | semidirect |
| 28. #18011831 | C22 | semidirect |
| 29. #18011821 | C22 | semidirect |
| 30. C4×#11924746 | C22 | semidirect |
| 31. C4⋊Q8×C149 | C22 | semidirect |
| 33. #102×C149 | C22 | semidirect |
| 34. C4×C8×C149 | C22 | semidirect |
| 123. C149 | #3138 | semidirect |
| 131. #486 | D149 | semidirect |
| 139. C4⋊Q8 | C2×D149 | semidirect |
| 155. #102 | C2×D149 | semidirect |
| 158. C4×C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750180 | 2 |
| #127×D149 | 2 |
| #23749988 | 2 |
| #23749973 | 2 |
| #23749972 | 2 |
| #23749971 | 2 |
| #23749628 | 2 |
| C4×#14558719 | 2 |
| #486×C149 | 2 |
| #3138 | 149 |