Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23750242 | C2 | semidirect |
| 2. #23750029 | C2 | semidirect |
| 3. #23750008 | C2 | semidirect |
| 4. #23749983 | C2 | semidirect |
| 5. #23749869 | C2 | semidirect |
| 6. #23749866 | C2 | semidirect |
| 7. #23749722 | C2 | semidirect |
| 8. #23749719 | C2 | semidirect |
| 9. D8×Dic149 | C2 | semidirect |
| 10. #23749580 | C2 | semidirect |
| 117. C149 | #3175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750242 | 2 |
| #23750029 | 2 |
| #23750008 | 2 |
| #23749983 | 2 |
| #23749869 | 2 |
| #23749866 | 2 |
| #23749722 | 2 |
| #23749719 | 2 |
| D8×Dic149 | 2 |
| #23749580 | 2 |
| #466×C149 | 2 |
| #3175 | 149 |