Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23750336 | C2 | semidirect |
| 3. #23749968 | C2 | semidirect |
| 4. #23749940 | C2 | semidirect |
| 5. #23749917 | C2 | semidirect |
| 6. #23749912 | C2 | semidirect |
| 7. #23749872 | C2 | semidirect |
| 8. C4×#14558725 | C2 | semidirect |
| 9. #23749704 | C2 | semidirect |
| 10. #23749666 | C2 | semidirect |
| 11. #500×C149 | C2 | semidirect |
| 121. C149 | #3357 | semidirect |
| 125. #500 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750341 | 2 |
| #23750336 | 2 |
| #23749968 | 2 |
| #23749940 | 2 |
| #23749917 | 2 |
| #23749912 | 2 |
| #23749872 | 2 |
| C4×#14558725 | 2 |
| #23749704 | 2 |
| #23749666 | 2 |
| #500×C149 | 2 |
| #3357 | 149 |