Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #23750099 | C2 | semidirect |
| 3. #23749735 | C2 | semidirect |
| 4. C4×#14558721 | C2 | semidirect |
| 5. #23749661 | C2 | semidirect |
| 6. #23749630 | C2 | semidirect |
| 7. #23749629 | C2 | semidirect |
| 8. #23749581 | C2 | semidirect |
| 9. #518×C149 | C2 | semidirect |
| 11. C2×#14558721 | C4 | semidirect |
| 16. C4×D596 | C22 | semidirect |
| 20. #18011844 | C22 | semidirect |
| 21. #18011842 | C22 | semidirect |
| 22. #18011832 | C22 | semidirect |
| 23. #18011831 | C22 | semidirect |
| 24. #18011822 | C22 | semidirect |
| 25. C4×#11924746 | C22 | semidirect |
| 28. C4×D4×C149 | C22 | semidirect |
| 35. C2×D596 | C2×C4 | semidirect |
| 38. #14558721 | C2×C4 | semidirect |
| 39. #14558721 | C2×C4 | semidirect |
| 41. C2×#11924746 | C2×C4 | semidirect |
| 52. C2×D4×C149 | C2×C4 | semidirect |
| 108. C149 | #2948 | semidirect |
| 112. #518 | D149 | semidirect |
| 129. C4×D4 | C2×D149 | semidirect |
| 149. C2×D4 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558721 | 2 |
| #23750099 | 2 |
| #23749735 | 2 |
| C4×#14558721 | 2 |
| #23749661 | 2 |
| #23749630 | 2 |
| #23749629 | 2 |
| #23749581 | 2 |
| #518×C149 | 2 |
| #2948 | 149 |