Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23750173 | C2 | semidirect |
| 2. #124×D149 | C2 | semidirect |
| 3. #23750012 | C2 | semidirect |
| 4. #23749985 | C2 | semidirect |
| 5. #23749984 | C2 | semidirect |
| 6. #23749842 | C2 | semidirect |
| 7. #23749838 | C2 | semidirect |
| 8. #23749762 | C2 | semidirect |
| 9. #23749757 | C2 | semidirect |
| 10. #23749680 | C2 | semidirect |
| 11. #496×C149 | C2 | semidirect |
| 15. C2×#14558724 | C22 | semidirect |
| 17. #18011911 | C22 | semidirect |
| 27. D4×Dic149 | C22 | semidirect |
| 31. #18011840 | C22 | semidirect |
| 32. #18011836 | C22 | semidirect |
| 33. #18011835 | C22 | semidirect |
| 37. #18011822 | C22 | semidirect |
| 38. C2×SD16×C149 | C22 | semidirect |
| 40. #127×C149 | C22 | semidirect |
| 42. #97×C149 | C22 | semidirect |
| 150. C149 | #3213 | semidirect |
| 155. #496 | D149 | semidirect |
| 167. C2×SD16 | C2×D149 | semidirect |
| 171. #127 | C2×D149 | semidirect |
| 193. #97 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750173 | 2 |
| #124×D149 | 2 |
| #23750012 | 2 |
| #23749985 | 2 |
| #23749984 | 2 |
| #23749842 | 2 |
| #23749838 | 2 |
| #23749762 | 2 |
| #23749757 | 2 |
| #23749680 | 2 |
| #496×C149 | 2 |
| #3213 | 149 |