Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750175 | C2 | semidirect |
| 2. #23750035 | C2 | semidirect |
| 3. #23750015 | C2 | semidirect |
| 4. #23749991 | C2 | semidirect |
| 5. #23749984 | C2 | semidirect |
| 6. #23749876 | C2 | semidirect |
| 7. #23749873 | C2 | semidirect |
| 8. C4×#14558723 | C2 | semidirect |
| 9. C4×#14558721 | C2 | semidirect |
| 10. C4×#14558720 | C2 | semidirect |
| 11. #529×C149 | C2 | semidirect |
| 92. #11924746 | #41 | semidirect |
| 137. C149 | #3171 | semidirect |
| 140. #529 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23750035 | 2 |
| #23750015 | 2 |
| #23749991 | 2 |
| #23749984 | 2 |
| #23749876 | 2 |
| #23749873 | 2 |
| C4×#14558723 | 2 |
| C4×#14558721 | 2 |
| C4×#14558720 | 2 |
| #529×C149 | 2 |
| #3171 | 149 |