Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 366 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. #23750181 | C2 | semidirect |
| 3. #23750031 | C2 | semidirect |
| 4. #23749991 | C2 | semidirect |
| 5. #23749990 | C2 | semidirect |
| 6. #23749952 | C2 | semidirect |
| 7. #23749951 | C2 | semidirect |
| 8. #23749914 | C2 | semidirect |
| 9. #23749904 | C2 | semidirect |
| 10. #23749680 | C2 | semidirect |
| 11. #501×C149 | C2 | semidirect |
| 128. C149 | #3235 | semidirect |
| 133. #501 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750181 | 2 |
| #23750176 | 2 |
| #23750031 | 2 |
| #23749991 | 2 |
| #23749990 | 2 |
| #23749952 | 2 |
| #23749951 | 2 |
| #23749914 | 2 |
| #23749904 | 2 |
| #23749680 | 2 |
| #501×C149 | 2 |
| #3235 | 149 |