Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23750028 | C2 | semidirect |
| 3. #23749958 | C2 | semidirect |
| 4. #23749949 | C2 | semidirect |
| 5. #23749910 | C2 | semidirect |
| 6. #23749902 | C2 | semidirect |
| 7. #23749873 | C2 | semidirect |
| 8. C4×#14558723 | C2 | semidirect |
| 9. #23749703 | C2 | semidirect |
| 10. #23749668 | C2 | semidirect |
| 11. #556×C149 | C2 | semidirect |
| 85. #11924746 | #41 | semidirect |
| 122. C149 | #3353 | semidirect |
| 124. #556 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750279 | 2 |
| #23750028 | 2 |
| #23749958 | 2 |
| #23749949 | 2 |
| #23749910 | 2 |
| #23749902 | 2 |
| #23749873 | 2 |
| C4×#14558723 | 2 |
| #23749703 | 2 |
| #23749668 | 2 |
| #556×C149 | 2 |
| #3353 | 149 |