Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23750175 | C2 | semidirect |
| 2. C2×C4×D596 | C2 | semidirect |
| 3. #23749944 | C2 | semidirect |
| 4. #23749916 | C2 | semidirect |
| 5. #23749821 | C2 | semidirect |
| 6. #23749761 | C2 | semidirect |
| 7. #23749738 | C2 | semidirect |
| 8. #432×C149 | C2 | semidirect |
| 13. #18011911 | C22 | semidirect |
| 14. #18011908 | C22 | semidirect |
| 23. C4×D596 | C22 | semidirect |
| 26. #18011843 | C22 | semidirect |
| 28. #18011833 | C22 | semidirect |
| 30. C4⋊C8×C149 | C22 | semidirect |
| 32. #97×C149 | C22 | semidirect |
| 76. D596 | #41 | semidirect |
| 120. C149 | #3109 | semidirect |
| 129. #432 | D149 | semidirect |
| 149. C4⋊C8 | C2×D149 | semidirect |
| 153. #97 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| C2×C4×D596 | 2 |
| #23749944 | 2 |
| #23749916 | 2 |
| #23749821 | 2 |
| #23749761 | 2 |
| #23749738 | 2 |
| #432×C149 | 2 |
| #3109 | 149 |