Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23750161 | C2 | semidirect |
| 2. C2×#18011900 | C2 | semidirect |
| 3. #23750010 | C2 | semidirect |
| 4. #23749981 | C2 | semidirect |
| 5. #23749849 | C2 | semidirect |
| 6. #23749843 | C2 | semidirect |
| 7. #23749775 | C2 | semidirect |
| 8. #23749764 | C2 | semidirect |
| 10. #23749675 | C2 | semidirect |
| 11. #451×C149 | C2 | semidirect |
| 14. C2×#14558723 | C22 | semidirect |
| 17. #18011902 | C22 | semidirect |
| 22. #18011900 | C22 | semidirect |
| 25. Q8×Dic149 | C22 | semidirect |
| 26. #18011873 | C22 | semidirect |
| 32. #18011840 | C22 | semidirect |
| 33. #18011835 | C22 | semidirect |
| 37. C8×Dic149 | C22 | semidirect |
| 39. C2×Q16×C149 | C22 | semidirect |
| 41. #103×C149 | C22 | semidirect |
| 143. C149 | #3211 | semidirect |
| 151. #451 | D149 | semidirect |
| 158. C2×Q16 | C2×D149 | semidirect |
| 181. #103 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750161 | 2 |
| C2×#18011900 | 2 |
| #23750010 | 2 |
| #23749981 | 2 |
| #23749849 | 2 |
| #23749843 | 2 |
| #23749775 | 2 |
| #23749764 | 2 |
| #23749761 | 2 |
| #23749675 | 2 |
| #451×C149 | 2 |
| #3211 | 149 |