Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23750180 | C2 | semidirect |
| 3. #23750034 | C2 | semidirect |
| 4. #23749993 | C2 | semidirect |
| 5. #23749984 | C2 | semidirect |
| 6. #23749880 | C2 | semidirect |
| 8. Q16×Dic149 | C2 | semidirect |
| 9. SD16×Dic149 | C2 | semidirect |
| 10. #23749577 | C2 | semidirect |
| 11. #497×C149 | C2 | semidirect |
| 129. C149 | #3172 | semidirect |
| 134. #497 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750180 | 2 |
| #23750154 | 2 |
| #23750034 | 2 |
| #23749993 | 2 |
| #23749984 | 2 |
| #23749880 | 2 |
| #23749868 | 2 |
| Q16×Dic149 | 2 |
| SD16×Dic149 | 2 |
| #23749577 | 2 |
| #497×C149 | 2 |
| #3172 | 149 |