Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 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. C2×#18011908 | C2 | semidirect |
| 2. #23750015 | C2 | semidirect |
| 3. #23749991 | C2 | semidirect |
| 4. #23749825 | C2 | semidirect |
| 5. #23749820 | C2 | semidirect |
| 6. #23749775 | C2 | semidirect |
| 7. #23749758 | C2 | semidirect |
| 8. #23749682 | C2 | semidirect |
| 9. #529×C149 | C2 | semidirect |
| 13. C2×#14558723 | C22 | semidirect |
| 14. C2×#14558721 | C22 | semidirect |
| 19. C4⋊#11924746 | C22 | semidirect |
| 20. #18011831 | C22 | semidirect |
| 21. #18011831 | C22 | semidirect |
| 23. #18011822 | C22 | semidirect |
| 25. #125×C149 | C22 | semidirect |
| 26. #124×C149 | C22 | semidirect |
| 30. C4×Q8×C149 | C22 | semidirect |
| 32. C4×D4×C149 | C22 | semidirect |
| 127. C149 | #3217 | semidirect |
| 130. #529 | D149 | semidirect |
| 148. #125 | C2×D149 | semidirect |
| 149. #124 | C2×D149 | semidirect |
| 153. C4×Q8 | C2×D149 | semidirect |
| 155. C4×D4 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011908 | 2 |
| #23750015 | 2 |
| #23749991 | 2 |
| #23749825 | 2 |
| #23749820 | 2 |
| #23749775 | 2 |
| #23749758 | 2 |
| #23749682 | 2 |
| #529×C149 | 2 |
| #3217 | 149 |