Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 2. #23750024 | C2 | semidirect |
| 3. #23749999 | C2 | semidirect |
| 4. #23749993 | C2 | semidirect |
| 5. #23749991 | C2 | semidirect |
| 6. #23749873 | C2 | semidirect |
| 7. #23749856 | C2 | semidirect |
| 8. #23749723 | C2 | semidirect |
| 9. C4×#14558723 | C2 | semidirect |
| 10. #23749581 | C2 | semidirect |
| 11. #541×C149 | C2 | semidirect |
| 108. C149 | #3174 | semidirect |
| 110. #541 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750230 | 2 |
| #23750024 | 2 |
| #23749999 | 2 |
| #23749993 | 2 |
| #23749991 | 2 |
| #23749873 | 2 |
| #23749856 | 2 |
| #23749723 | 2 |
| C4×#14558723 | 2 |
| #23749581 | 2 |
| #541×C149 | 2 |
| #3174 | 149 |