Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23750136 | C2 | semidirect |
| 2. #23749967 | C2 | semidirect |
| 3. #23749950 | C2 | semidirect |
| 4. #23749866 | C2 | semidirect |
| 5. #23749861 | C2 | semidirect |
| 6. #23749854 | C2 | semidirect |
| 7. #23749789 | C2 | semidirect |
| 8. #23749772 | C2 | semidirect |
| 9. C2×C22⋊C8×C149 | C2 | semidirect |
| 11. C2×Dic596 | C22 | semidirect |
| 12. C2×#14558725 | C22 | semidirect |
| 13. C2×D1192 | C22 | semidirect |
| 23. #18011845 | C22 | semidirect |
| 24. #18011845 | C22 | semidirect |
| 25. #18011843 | C22 | semidirect |
| 26. #18011836 | C22 | semidirect |
| 27. #18011836 | C22 | semidirect |
| 28. #18011833 | C22 | semidirect |
| 29. #18011833 | C22 | semidirect |
| 121. C149 | #3191 | semidirect |
| 131. C2×C22⋊C8 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750136 | 2 |
| #23749967 | 2 |
| #23749950 | 2 |
| #23749866 | 2 |
| #23749861 | 2 |
| #23749854 | 2 |
| #23749789 | 2 |
| #23749772 | 2 |
| C2×C22⋊C8×C149 | 2 |
| #3191 | 149 |