Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
292 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 3. #23749580 | C2 | semidirect |
| 4. C2×#18011821 | C2 | semidirect |
| 5. #23749389 | C2 | semidirect |
| 6. #23749386 | C2 | semidirect |
| 12. #18011838 | C4 | semidirect |
| 13. #18011835 | C4 | semidirect |
| 14. #18011832 | C4 | semidirect |
| 20. #131×C149 | C4 | semidirect |
| 98. C149 | #1765 | semidirect |
| 109. #131 | Dic149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011838 | 2 |
| #23749621 | 2 |
| #23749580 | 2 |
| C2×#18011821 | 2 |
| #23749389 | 2 |
| #23749386 | 2 |
| C2×#131×C149 | 2 |
| #1765 | 149 |