Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. #23750336 | C2 | semidirect |
| 3. #23749973 | C2 | semidirect |
| 4. #23749945 | C2 | semidirect |
| 5. #23749855 | C2 | semidirect |
| 6. #23749826 | C2 | semidirect |
| 7. #23749777 | C2 | semidirect |
| 8. C4×#14558724 | C2 | semidirect |
| 9. #23749690 | C2 | semidirect |
| 10. #102×D149 | C2 | semidirect |
| 11. #476×C149 | C2 | semidirect |
| 14. C2×#14558725 | C22 | semidirect |
| 16. C2×C8×D149 | C22 | semidirect |
| 19. #18011891 | C22 | semidirect |
| 24. C4×Dic298 | C22 | semidirect |
| 27. C4⋊C4×D149 | C22 | semidirect |
| 28. #18011842 | C22 | semidirect |
| 29. #18011834 | C22 | semidirect |
| 30. #18011833 | C22 | semidirect |
| 32. #18011831 | C22 | semidirect |
| 33. #18011831 | C22 | semidirect |
| 34. #18011823 | C22 | semidirect |
| 35. C4×#11924746 | C22 | semidirect |
| 36. C4⋊Q8×C149 | C22 | semidirect |
| 38. #106×C149 | C22 | semidirect |
| 39. C4⋊C8×C149 | C22 | semidirect |
| 89. D596 | SD16 | semidirect |
| 136. C149 | #3295 | semidirect |
| 142. #476 | D149 | semidirect |
| 154. C4⋊Q8 | C2×D149 | semidirect |
| 168. #106 | C2×D149 | semidirect |
| 169. C4⋊C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750336 | 2 |
| D4×D596 | 2 |
| #23749973 | 2 |
| #23749945 | 2 |
| #23749855 | 2 |
| #23749826 | 2 |
| #23749777 | 2 |
| C4×#14558724 | 2 |
| #23749690 | 2 |
| #102×D149 | 2 |
| #476×C149 | 2 |
| #3295 | 149 |