Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 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. C2×Q8×Dic149 | C2 | semidirect |
| 3. #23749961 | C2 | semidirect |
| 5. #23749934 | C2 | semidirect |
| 6. #23749845 | C2 | semidirect |
| 7. #23749781 | C2 | semidirect |
| 8. #23749729 | C2 | semidirect |
| 9. #23749726 | C2 | semidirect |
| 10. #23749679 | C2 | semidirect |
| 131. C149 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750156 | 2 |
| C2×Q8×Dic149 | 2 |
| #23749961 | 2 |
| #23749941 | 2 |
| #23749934 | 2 |
| #23749845 | 2 |
| #23749781 | 2 |
| #23749729 | 2 |
| #23749726 | 2 |
| #23749679 | 2 |
| #448×C149 | 2 |
| #3117 | 149 |